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Sample records for quantum mechanics based

  1. Quantum mechanics

    International Nuclear Information System (INIS)

    Rae, A.I.M.

    1981-01-01

    This book, based on a thirty lecture course given to students at the beginning of their second year, covers the quantum mechanics required by physics undergraduates. Early chapters deal with wave mechanics, including a discussion of the energy states of the hydrogen atom. These are followed by a more formal development of the theory, leading to a discussion of some advanced applications and an introduction to the conceptual problems associated with quantum measurement theory. Emphasis is placed on the fundamentals of quantum mechanics. Problems are included at the end of each chapter. (U.K.)

  2. Quantum mechanics

    CERN Document Server

    Powell, John L

    2015-01-01

    Suitable for advanced undergraduates, this thorough text focuses on the role of symmetry operations and the essentially algebraic structure of quantum-mechanical theory. Based on courses in quantum mechanics taught by the authors, the treatment provides numerous problems that require applications of theory and serve to supplement the textual material.Starting with a historical introduction to the origins of quantum theory, the book advances to discussions of the foundations of wave mechanics, wave packets and the uncertainty principle, and an examination of the Schrödinger equation that includ

  3. Quantum mechanics symmetries

    CERN Document Server

    Greiner, Walter

    1989-01-01

    "Quantum Dynamics" is a major survey of quantum theory based on Walter Greiner's long-running and highly successful courses at the University of Frankfurt. The key to understanding in quantum theory is to reinforce lecture attendance and textual study by working through plenty of representative and detailed examples. Firm belief in this principle led Greiner to develop his unique course and to transform it into a remarkable and comprehensive text. The text features a large number of examples and exercises involving many of the most advanced topics in quantum theory. These examples give practical and precise demonstrations of how to use the often subtle mathematics behind quantum theory. The text is divided into five volumes: Quantum Mechanics I - An Introduction, Quantum Mechanics II - Symmetries, Relativistic Quantum Mechanics, Quantum Electrodynamics, Gauge Theory of Weak Interactions. These five volumes take the reader from the fundamental postulates of quantum mechanics up to the latest research in partic...

  4. Fractional quantum mechanics

    CERN Document Server

    Laskin, Nick

    2018-01-01

    Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics. This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder. The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework. Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process. The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique...

  5. p-Adic quantum mechanics

    International Nuclear Information System (INIS)

    Vladimirov, V.S.; Volovich, I.V.

    1988-01-01

    Quantum mechanics above the field of p-adic numbers is constructed. Three formulations of p-adic quantum mechanics are considered: 1) quantum mechanics with complex-valued wave functions and p-adic coordinates and pulses; an approach based on Weyl representation is suggested; 2) the probability (Euclidean) formulation; 3) the secondary quantization representation (Fock representation) with p-adic wave functions

  6. Non-relativistic quantum mechanics

    CERN Document Server

    Puri, Ravinder R

    2017-01-01

    This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...

  7. Testing Nonassociative Quantum Mechanics.

    Science.gov (United States)

    Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut

    2015-11-27

    The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

  8. Quantum control mechanism analysis through field based Hamiltonian encoding

    International Nuclear Information System (INIS)

    Mitra, Abhra; Rabitz, Herschel

    2006-01-01

    Optimal control of quantum dynamics in the laboratory is proving to be increasingly successful. The control fields can be complex, and the mechanisms by which they operate have often remained obscure. Hamiltonian encoding (HE) has been proposed as a method for understanding mechanisms in quantum dynamics. In this context mechanism is defined in terms of the dominant quantum pathways leading to the final state of the controlled system. HE operates by encoding a special modulation into the Hamiltonian and decoding its signature in the dynamics to determine the dominant pathway amplitudes. Earlier work encoded the modulation directly into the Hamiltonian operators. This present work introduces the alternative scheme of field based HE, where the modulation is encoded into the control field and not directly into the Hamiltonian operators. This distinct form of modulation yields a new perspective on mechanism and is computationally faster than the earlier approach. Field based encoding is also an important step towards a laboratory based algorithm for HE as it is the only form of encoding that may be experimentally executed. HE is also extended to cover systems with noise and uncertainty and finally, a hierarchical algorithm is introduced to reveal mechanism in a stepwise fashion of ever increasing detail as desired. This new hierarchical algorithm is an improvement over earlier approaches to HE where the entire mechanism was determined in one stroke. The improvement comes from the use of less complex modulation schemes, which leads to fewer evaluations of Schroedinger's equation. A number of simulations are presented on simple systems to illustrate the new field based encoding technique for mechanism assessment

  9. Quantum mechanics

    International Nuclear Information System (INIS)

    Anon.

    1990-01-01

    The book is on quantum mechanics. The emphasis is on the basic concepts and the methodology. The chapters include: Breakdown of classical concepts; Quantum mechanical concepts; Basic postulates of quantum mechanics; solution of problems in quantum mechanics; Simple harmonic oscillator; and Angular Momentum

  10. Quantum opto-mechanics with micromirrors : combining nano-mechanics with quantum optics

    International Nuclear Information System (INIS)

    Groeblacher, S.

    2010-01-01

    exchange between the optical and the mechanical subsystems is possible, as their coupling rate is bigger than their individual decoherence rates. This experiment is an important milestone in showing macroscopic mechanical quantum behavior. Finally, we have performed an experiment where we have measured the optomechanical correlations. The correlations are used for probing radiation-pressure based down-conversion and such an experiment will ultimately allow the generation and detection of entanglement between the optical and the mechanical system. (author) [de

  11. Quantum mechanics

    International Nuclear Information System (INIS)

    Basdevant, J.L.; Dalibard, J.; Joffre, M.

    2008-01-01

    All physics is quantum from elementary particles to stars and to the big-bang via semi-conductors and chemistry. This theory is very subtle and we are not able to explain it without the help of mathematic tools. This book presents the principles of quantum mechanics and describes its mathematical formalism (wave function, Schroedinger equation, quantum operators, spin, Hamiltonians, collisions,..). We find numerous applications in the fields of new technologies (maser, quantum computer, cryptography,..) and in astrophysics. A series of about 90 exercises with their answers is included. This book is based on a physics course at a graduate level. (A.C.)

  12. A probabilistic approach to quantum mechanics based on 'tomograms'

    International Nuclear Information System (INIS)

    Caponigro, M.; Mancini, S.; Man'ko, V.I.

    2006-01-01

    It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function and density operator. The relevant concepts of quantum mechanics are then reconsidered and the epistemological implications of such approach discussed. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  13. Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics

    International Nuclear Information System (INIS)

    Goldfarb, Yair; Degani, Ilan; Tannor, David J.

    2006-01-01

    In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared--it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification - a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynamics to give exact quantum mechanics. We demonstrate tunneling probabilities that are in virtually perfect agreement with the exact quantum mechanics down to 10 -7 calculated from strictly localized quantum trajectories that do not communicate with their neighbors. The new formulation may have significant implications for fundamental quantum mechanics, ranging from the interpretation of non-locality to measures of quantum complexity

  14. Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation

    International Nuclear Information System (INIS)

    Znojil, Miloslav

    2004-01-01

    Witten's the non-relativistic formalism of supersymmetric quantum mechanics was based on a factorization and partnership between Schroedinger equations. We show how it accommodates a transition to the partnership between relativistic Klein-Gordon equations

  15. Statistical ensembles in quantum mechanics

    International Nuclear Information System (INIS)

    Blokhintsev, D.

    1976-01-01

    The interpretation of quantum mechanics presented in this paper is based on the concept of quantum ensembles. This concept differs essentially from the canonical one by that the interference of the observer into the state of a microscopic system is of no greater importance than in any other field of physics. Owing to this fact, the laws established by quantum mechanics are not of less objective character than the laws governing classical statistical mechanics. The paradoxical nature of some statements of quantum mechanics which result from the interpretation of the wave functions as the observer's notebook greatly stimulated the development of the idea presented. (Auth.)

  16. Extended quantum mechanics

    International Nuclear Information System (INIS)

    Pavel Bona

    2000-01-01

    The work can be considered as an essay on mathematical and conceptual structure of nonrelativistic quantum mechanics which is related here to some other (more general, but also to more special and 'approximative') theories. Quantum mechanics is here primarily reformulated in an equivalent form of a Poisson system on the phase space consisting of density matrices, where the 'observables', as well as 'symmetry generators' are represented by a specific type of real valued (densely defined) functions, namely the usual quantum expectations of corresponding selfjoint operators. It is shown in this paper that inclusion of additional ('nonlinear') symmetry generators (i. e. 'Hamiltonians') into this reformulation of (linear) quantum mechanics leads to a considerable extension of the theory: two kinds of quantum 'mixed states' should be distinguished, and operator - valued functions of density matrices should be used in the role of 'nonlinear observables'. A general framework for physical theories is obtained in this way: By different choices of the sets of 'nonlinear observables' we obtain, as special cases, e.g. classical mechanics on homogeneous spaces of kinematical symmetry groups, standard (linear) quantum mechanics, or nonlinear extensions of quantum mechanics; also various 'quasiclassical approximations' to quantum mechanics are all sub theories of the presented extension of quantum mechanics - a version of the extended quantum mechanics. A general interpretation scheme of extended quantum mechanics extending the usual statistical interpretation of quantum mechanics is also proposed. Eventually, extended quantum mechanics is shown to be (included into) a C * -algebraic (hence linear) quantum theory. Mathematical formulation of these theories is presented. The presentation includes an analysis of problems connected with differentiation on infinite-dimensional manifolds, as well as a solution of some problems connected with the work with only densely defined unbounded

  17. Applications of quantum mechanical techniques to areas outside of quantum mechanics

    CERN Document Server

    Khrennikov, Andrei

    2018-01-01

    This book deals with applications of quantum mechanical techniques to areas outside of quantum mechanics, so-called quantum-like modeling. Research in this area has grown over the last 15 years. But even already more than 50 years ago, the interaction between Physics Nobelist Pauli and the psychologist Carl Jung in the 1950's on seeking to find analogous uses of the complementarity principle from quantum mechanics in psychology needs noting. This book does NOT want to advance that society is quantum mechanical! The macroscopic world is manifestly not quantum mechanical. But this rules not out that one can use concepts and the mathematical apparatus from quantum physics in a macroscopic environment. A mainstay ingredient of quantum mechanics, is 'quantum probability' and this tool has been proven to be useful in the mathematical modelling of decision making. In the most basic experiment of quantum physics, the double slit experiment, it is known (from the works of A. Khrennikov) that the law of total probabi...

  18. The birth and growth of quantum theory. From quantum hypothesis to quantum mechanics

    International Nuclear Information System (INIS)

    Peng Huanwu

    2001-01-01

    The short history covers the birth and early growth of quantum theory from 1900 to 1928, beginning with Planck's formula and the quantum hypothesis for the black-body radiation. After a description of the rise and decline of the old quantum theory in connection with its application in spectroscopy, two paths based on the rigorous formulation of the correspondence principle leading to matrix mechanics (1925) and Dirac's non-commuting q-numbers (1925) are explained. Another path based on the generalization of the wave-particle aspect of light quanta is then shown to lead to wave mechanics (1926). Among the works during the early growth of quantum mechanics in 1927-1928, representation theory, the uncertainty principle, two-electron problems, and Dirac's relativistic theory of electrons are discussed

  19. Engineering quantum mechanics

    CERN Document Server

    Ahn, Doyeol

    2011-01-01

    A clear introduction to quantum mechanics concepts Quantum mechanics has become an essential tool for modern engineering, particularly due to the recent developments in quantum computing as well as the rapid progress in optoelectronic devices. Engineering Quantum Mechanics explains the fundamentals of this exciting field, providing broad coverage of both traditional areas such as semiconductor and laser physics as well as relatively new yet fast-growing areas such as quantum computation and quantum information technology. The book begins with basic quantum mechanics, reviewing measurements and probability, Dirac formulation, the uncertainty principle, harmonic oscillator, angular momentum eigenstates, and perturbation theory. Then, quantum statistical mechanics is explored, from second quantization and density operators to coherent and squeezed states, coherent interactions between atoms and fields, and the Jaynes-Cummings model. From there, the book moves into elementary and modern applications, discussing s...

  20. Quantum mechanics

    CERN Document Server

    Rae, Alastair I M

    2016-01-01

    A Thorough Update of One of the Most Highly Regarded Textbooks on Quantum Mechanics Continuing to offer an exceptionally clear, up-to-date treatment of the subject, Quantum Mechanics, Sixth Edition explains the concepts of quantum mechanics for undergraduate students in physics and related disciplines and provides the foundation necessary for other specialized courses. This sixth edition builds on its highly praised predecessors to make the text even more accessible to a wider audience. It is now divided into five parts that separately cover broad topics suitable for any general course on quantum mechanics. New to the Sixth Edition * Three chapters that review prerequisite physics and mathematics, laying out the notation, formalism, and physical basis necessary for the rest of the book * Short descriptions of numerous applications relevant to the physics discussed, giving students a brief look at what quantum mechanics has made possible industrially and scientifically * Additional end-of-chapter problems with...

  1. Elementary quantum mechanics

    CERN Document Server

    Saxon, David S

    2012-01-01

    Based on lectures for an undergraduate UCLA course in quantum mechanics, this volume focuses on the formulas of quantum mechanics rather than applications. Widely used in both upper-level undergraduate and graduate courses, it offers a broad self-contained survey rather than in-depth treatments.Topics include the dual nature of matter and radiation, state functions and their interpretation, linear momentum, the motion of a free particle, Schrödinger's equation, approximation methods, angular momentum, and many other subjects. In the interests of keeping the mathematics as simple as possible, m

  2. Protein structure refinement using a quantum mechanics-based chemical shielding predictor

    DEFF Research Database (Denmark)

    Bratholm, Lars Andersen; Jensen, Jan Halborg

    2017-01-01

    The accurate prediction of protein chemical shifts using a quantum mechanics (QM)-based method has been the subject of intense research for more than 20 years but so far empirical methods for chemical shift prediction have proven more accurate. In this paper we show that a QM-based predictor...... of a protein backbone and CB chemical shifts (ProCS15, PeerJ, 2016, 3, e1344) is of comparable accuracy to empirical chemical shift predictors after chemical shift-based structural refinement that removes small structural errors. We present a method by which quantum chemistry based predictions of isotropic...

  3. On obtaining classical mechanics from quantum mechanics

    International Nuclear Information System (INIS)

    Date, Ghanashyam

    2007-01-01

    Constructing a classical mechanical system associated with a given quantum-mechanical one entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of coarser observations. The Hilbert space of any quantum-mechanical system naturally has the structure of an infinite-dimensional symplectic manifold ('quantum phase space'). There is also a systematic, quotienting procedure which imparts a bundle structure to the quantum phase space and extracts a classical phase space as the base space. This works straightforwardly when the Hilbert space carries weakly continuous representation of the Heisenberg group and one recovers the linear classical phase space R 2N . We report on how the procedure also allows extraction of nonlinear classical phase spaces and illustrate it for Hilbert spaces being finite dimensional (spin-j systems), infinite dimensional but separable (particle on a circle) and infinite dimensional but non-separable (polymer quantization). To construct a corresponding classical dynamics, one needs to choose a suitable section and identify an effective Hamiltonian. The effective dynamics mirrors the quantum dynamics provided the section satisfies conditions of semiclassicality and tangentiality

  4. Teaching Quantum Mechanics on an Introductory Level.

    Science.gov (United States)

    Muller, Rainer; Wiesner, Hartmut

    2002-01-01

    Presents a new research-based course on quantum mechanics in which the conceptual issues of quantum mechanics are taught at an introductory level. Involves students in the discovery of how quantum phenomena deviate from classical everyday experiences. (Contains 31 references.) (Author/YDS)

  5. Quantum mechanics for applied physics and engineering

    CERN Document Server

    Fromhold, Albert T

    2011-01-01

    This excellent text, directed to upper-level undergraduates and graduate students in engineering and applied physics, introduces the fundamentals of quantum mechanics, emphasizing those aspects of quantum mechanics and quantum statistics essential to an understanding of solid-state theory. A heavy background in mathematics and physics is not required beyond basic courses in calculus, differential equations, and calculus-based elementary physics.The first three chapters introduce quantum mechanics (using the Schrödinger equations), quantum statistics, and the free-electron theory of metals. Ch

  6. Learn Quantum Mechanics with Haskell

    Directory of Open Access Journals (Sweden)

    Scott N. Walck

    2016-11-01

    Full Text Available To learn quantum mechanics, one must become adept in the use of various mathematical structures that make up the theory; one must also become familiar with some basic laboratory experiments that the theory is designed to explain. The laboratory ideas are naturally expressed in one language, and the theoretical ideas in another. We present a method for learning quantum mechanics that begins with a laboratory language for the description and simulation of simple but essential laboratory experiments, so that students can gain some intuition about the phenomena that a theory of quantum mechanics needs to explain. Then, in parallel with the introduction of the mathematical framework on which quantum mechanics is based, we introduce a calculational language for describing important mathematical objects and operations, allowing students to do calculations in quantum mechanics, including calculations that cannot be done by hand. Finally, we ask students to use the calculational language to implement a simplified version of the laboratory language, bringing together the theoretical and laboratory ideas.

  7. Individuation in Quantum Mechanics and Space-Time

    Science.gov (United States)

    Jaeger, Gregg

    2010-10-01

    Two physical approaches—as distinct, under the classification of Mittelstaedt, from formal approaches—to the problem of individuation of quantum objects are considered, one formulated in spatiotemporal terms and one in quantum mechanical terms. The spatiotemporal approach itself has two forms: one attributed to Einstein and based on the ontology of space-time points, and the other proposed by Howard and based on intersections of world lines. The quantum mechanical approach is also provided here in two forms, one based on interference and another based on a new Quantum Principle of Individuation (QPI). It is argued that the space-time approach to individuation fails and that the quantum approach offers several advantages over it, including consistency with Leibniz’s Principle of Identity of Indiscernibles.

  8. Quantumness beyond quantum mechanics

    International Nuclear Information System (INIS)

    Sanz, Ángel S

    2012-01-01

    Bohmian mechanics allows us to understand quantum systems in the light of other quantum traits than the well-known ones (coherence, diffraction, interference, tunnelling, discreteness, entanglement, etc.). Here the discussion focusses precisely on two of these interesting aspects, which arise when quantum mechanics is thought within this theoretical framework: the non-crossing property, which allows for distinguishability without erasing interference patterns, and the possibility to define quantum probability tubes, along which the probability remains constant all the way. Furthermore, taking into account this hydrodynamic-like description as a link, it is also shown how this knowledge (concepts and ideas) can be straightforwardly transferred to other fields of physics (for example, the transmission of light along waveguides).

  9. Emergent mechanics, quantum and un-quantum

    Science.gov (United States)

    Ralston, John P.

    2013-10-01

    There is great interest in quantum mechanics as an "emergent" phenomenon. The program holds that nonobvious patterns and laws can emerge from complicated physical systems operating by more fundamental rules. We find a new approach where quantum mechanics itself should be viewed as an information management tool not derived from physics nor depending on physics. The main accomplishment of quantum-style theory comes in expanding the notion of probability. We construct a map from macroscopic information as data" to quantum probability. The map allows a hidden variable description for quantum states, and efficient use of the helpful tools of quantum mechanics in unlimited circumstances. Quantum dynamics via the time-dependent Shroedinger equation or operator methods actually represents a restricted class of classical Hamiltonian or Lagrangian dynamics, albeit with different numbers of degrees of freedom. We show that under wide circumstances such dynamics emerges from structureless dynamical systems. The uses of the quantum information management tools are illustrated by numerical experiments and practical applications

  10. Progress in post-quantum mechanics

    Science.gov (United States)

    Sarfatti, Jack

    2017-05-01

    Newton's mechanics in the 17th century increased the lethality of artillery. Thermodynamics in the 19th led to the steam-powered industrial revolution. Maxwell's unification of electricity, magnetism and light gave us electrical power, the telegraph, radio and television. The discovery of quantum mechanics in the 20th century by Planck, Bohr, Einstein, Schrodinger, Heisenberg led to the creation of the atomic and hydrogen bombs as well as computer chips, the world-wide-web and Silicon Valley's multibillion dollar corporations. The lesson is that breakthroughs in fundamental physics, both theoretical and experimental, have always led to profound technological wealth-creating industries and will continue to do so. There is now a new revolution brewing in quantum mechanics that can be divided into three periods. The first quantum revolution was from 1900 to about 1975. The second quantum information/computer revolution was from about 1975 to 2015. (The early part of this story is told by Kaiser in his book, How the Hippies Saved Physics, how a small group of Berkeley/San Francisco physicists triggered that second revolution.) The third quantum revolution is how an extension of quantum mechanics may lead to the understanding of consciousness as a natural physical phenomenon that can emerge in many material substrates, not only in our carbon-based biochemistry. In particular, this new post-quantum mechanics may lead to naturally conscious artificial intelligence in nano-electronic machines, as well as perhaps extending human life spans to hundreds of years and more.

  11. Probable Inference and Quantum Mechanics

    International Nuclear Information System (INIS)

    Grandy, W. T. Jr.

    2009-01-01

    In its current very successful interpretation the quantum theory is fundamentally statistical in nature. Although commonly viewed as a probability amplitude whose (complex) square is a probability, the wavefunction or state vector continues to defy consensus as to its exact meaning, primarily because it is not a physical observable. Rather than approach this problem directly, it is suggested that it is first necessary to clarify the precise role of probability theory in quantum mechanics, either as applied to, or as an intrinsic part of the quantum theory. When all is said and done the unsurprising conclusion is that quantum mechanics does not constitute a logic and probability unto itself, but adheres to the long-established rules of classical probability theory while providing a means within itself for calculating the relevant probabilities. In addition, the wavefunction is seen to be a description of the quantum state assigned by an observer based on definite information, such that the same state must be assigned by any other observer based on the same information, in much the same way that probabilities are assigned.

  12. Quantum mechanics with quantum time

    International Nuclear Information System (INIS)

    Kapuscik, E.

    1984-01-01

    Using a non-canonical Lie structure of classical mechanics a new algebra of quantum mechanical observables is constructed. The new algebra, in addition to the notion of classical time, makes it possible to introduce the notion of quantum time. A new type of uncertainty relation is derived. (author)

  13. Advanced Visual Quantum Mechanics

    CERN Document Server

    Thaller, Bernd

    2005-01-01

    Advanced Visual Quantum Mechanics is a systematic effort to investigate and to teach quantum mechanics with the aid of computer-generated animations. It is a self-contained textbook that combines selected topics from atomic physics (spherical symmetry, the hydrogen atom, and particles with spin) with an introduction to quantum information theory (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the strange behavior of Dirac equation solutions. A series of appendices covers important topics from perturbation and scattering theory. The book places an emphasis on ideas and concepts, with a fair to moderate amount of mathematical rigor. Though this book stands alone, it can also be paired with Thaller Visual Quantum Mechanics to form a comprehensive course in quantum mechanics. The software for the first book earned the European Academic Software Award 2000 for outstanding innovation in its field.

  14. Quantum physics, fuzzy sets and logic steps towards a many-valued interpretation of quantum mechanics

    CERN Document Server

    Pykacz, Jarosław

    2015-01-01

    This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of Łukasiewicz infinite-valued logic. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of many-valued logics and previous attempts to apply them for the description of quantum phenomena. The prospective many-valued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic representation of Birkhoff-von Neumann quantum logic in the form of a special Łukasiewicz infinite-valued logic endowed with partially defined conjunctions and disjunctions.

  15. Conceptual Foundations of Quantum Mechanics:. the Role of Evidence Theory, Quantum Sets, and Modal Logic

    Science.gov (United States)

    Resconi, Germano; Klir, George J.; Pessa, Eliano

    Recognizing that syntactic and semantic structures of classical logic are not sufficient to understand the meaning of quantum phenomena, we propose in this paper a new interpretation of quantum mechanics based on evidence theory. The connection between these two theories is obtained through a new language, quantum set theory, built on a suggestion by J. Bell. Further, we give a modal logic interpretation of quantum mechanics and quantum set theory by using Kripke's semantics of modal logic based on the concept of possible worlds. This is grounded on previous work of a number of researchers (Resconi, Klir, Harmanec) who showed how to represent evidence theory and other uncertainty theories in terms of modal logic. Moreover, we also propose a reformulation of the many-worlds interpretation of quantum mechanics in terms of Kripke's semantics. We thus show how three different theories — quantum mechanics, evidence theory, and modal logic — are interrelated. This opens, on one hand, the way to new applications of quantum mechanics within domains different from the traditional ones, and, on the other hand, the possibility of building new generalizations of quantum mechanics itself.

  16. A New Perspective on Relativistic Quantum Mechanics

    International Nuclear Information System (INIS)

    Kong, Otto C W

    2011-01-01

    Based on a linear realization formulation of a quantum relativity, - proposed relativity for 'quantum space-time', we introduce the new Poincare-Snyder relativity and Snyder relativity as relativities in between the latter and the well known Galilean and Einstein cases. While there is supposed to be not separate notion of classical and quantum mechanics at the level of the very unconventional quantum relativity, the Poincare-Snyder relativity is more like a mathematically extended form of Einstein relativity on which we can write down a formal canonical classical and quantum mechanics. We discuss how the Poincare-Snyder relativity may provide a stronger framework for the description of the usual (Einstein) relativistic quantum mechanics and present a first look of the interesting picture from the new perspective.

  17. Mathematical foundation of quantum mechanics

    CERN Document Server

    Parthasarathy, K R

    2005-01-01

    This is a brief introduction to the mathematical foundations of quantum mechanics based on lectures given by the author to Ph.D.students at the Delhi Centre of the Indian Statistical Institute in order to initiate active research in the emerging field of quantum probability. The material in the first chapter is included in the author's book "An Introduction to Quantum Stochastic Calculus" published by Birkhauser Verlag in 1992 and the permission of the publishers to reprint it here is acknowledged. Apart from quantum probability, an understanding of the role of group representations in the development of quantum mechanics is always a fascinating theme for mathematicians. The first chapter deals with the definitions of states, observables and automorphisms of a quantum system through Gleason's theorem, Hahn-Hellinger theorem and Wigner's theorem. Mackey's imprimitivity theorem and the theorem of inducing representations of groups in stages are proved directly for projective unitary antiunitary representations ...

  18. Quantum mechanics. An introduction

    International Nuclear Information System (INIS)

    Lesch, H.

    2008-01-01

    The following topics are dealt with: The way to quantum mechanics starting from thermal radiation and the stability of matter, Heisenberg's uncertainty relation, the impact of quantum mechanics on technology, the description of the big bang by means of quantum mechanics

  19. Cartoon computation: quantum-like computing without quantum mechanics

    International Nuclear Information System (INIS)

    Aerts, Diederik; Czachor, Marek

    2007-01-01

    We present a computational framework based on geometric structures. No quantum mechanics is involved, and yet the algorithms perform tasks analogous to quantum computation. Tensor products and entangled states are not needed-they are replaced by sets of basic shapes. To test the formalism we solve in geometric terms the Deutsch-Jozsa problem, historically the first example that demonstrated the potential power of quantum computation. Each step of the algorithm has a clear geometric interpretation and allows for a cartoon representation. (fast track communication)

  20. Quantum mechanics

    CERN Document Server

    Fitzpatrick, Richard

    2015-01-01

    Quantum mechanics was developed during the first few decades of the twentieth century via a series of inspired guesses made by various physicists, including Planck, Einstein, Bohr, Schroedinger, Heisenberg, Pauli, and Dirac. All these scientists were trying to construct a self-consistent theory of microscopic dynamics that was compatible with experimental observations. The purpose of this book is to present quantum mechanics in a clear, concise, and systematic fashion, starting from the fundamental postulates, and developing the theory in as logical manner as possible. Topics covered in the book include the fundamental postulates of quantum mechanics, angular momentum, time-dependent and time-dependent perturbation theory, scattering theory, identical particles, and relativistic electron theory.

  1. Classicality in quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Dreyer, Olaf [Theoretical Physics, Blackett Laboratory, Imperial College London, London, SW7 2AZ (United Kingdom)

    2007-05-15

    In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity.

  2. Classicality in quantum mechanics

    International Nuclear Information System (INIS)

    Dreyer, Olaf

    2007-01-01

    In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity

  3. Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

    International Nuclear Information System (INIS)

    Plotnitsky, Arkady

    2014-01-01

    This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well. (paper)

  4. Quantum mechanics and precision measurements

    International Nuclear Information System (INIS)

    Ramsey, N.F.

    1995-01-01

    The accuracies of measurements of almost all fundamental physical constants have increased by factors of about 10000 during the past 60 years. Although some of the improvements are due to greater care, most are due to new techniques based on quantum mechanics. Although the Heisenberg Uncertainty Principle often limits measurement accuracies, in many cases the validity of quantum mechanics makes possible the vastly improved measurement accuracies. Seven quantum features that have a profound influence on the science of measurements are: 1) Existence of discrete quantum states of energy. 2) Energy conservation in transitions between two states. 3) Electromagnetic radiation of frequency v is quantized with energy hv per quantum. 4) The identity principle. 5) The Heisenberg Uncertainty Principle. 6) Addition of probability amplitudes (not probabilities). 7) Wave and coherent phase phenomena. Of these seven quantum features, only the Heisenberg Uncertainty Principle limits the accuracy of measurements, and its effect is often negligibly small. The other six features make possible much more accurate measurements of quantum systems than with almost all classical systems. These effects are discussed and illustrated

  5. Relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Ollitrault, J.Y.

    1998-12-01

    These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.)

  6. Testing the foundations of quantum mechanics

    CERN Document Server

    Gisin, Nicolas; CERN. Geneva

    1999-01-01

    Quantum mechanics is certainly one of the most fascinating field of physics. In recent years, the new field of "quantum information processing" based on the most fundamental aspect of quantum mechanics, like linearity and entanglement, even increased and its peculiarities. In this series of 4 lectures we shall present some of the issues and experiments that test quantum theory. Entanglement leads, on the one hand side, to the measurement problem, to the EPR paradox and to quantum nonlocality ( distant systems). We will derive the Bell inequality, present experimental results that provide huge evidence in favor of quantum nonlocality and discuss some loopholes that are still open. On the other side, entanglement offers many new possibilities for information processing. Indeed, it provides means to carry out tasks that are either impossible classically (like quantum cryptography and quantum teleportation) or that would require significantly more steps to perform on a classical computer (like searching a databas...

  7. Quantum mechanics for pedestrians

    CERN Document Server

    Pade, Jochen

    2014-01-01

    This book provides an introduction into the fundamentals of non-relativistic quantum mechanics. In Part 1, the essential principles are developed. Applications and extensions of the formalism can be found in Part 2. The book includes not only material that is presented in traditional textbooks on quantum mechanics, but also discusses in detail current issues such as interaction-free quantum measurements, neutrino oscillations, various topics in the field of quantum information as well as fundamental problems and epistemological questions, such as the measurement problem, entanglement, Bell's inequality, decoherence, and the realism debate. A chapter on current interpretations of quantum mechanics concludes the book. To develop quickly and clearly the main principles of quantum mechanics and its mathematical formulation, there is a systematic change between wave mechanics and algebraic representation in the first chapters. The required mathematical tools are introduced step by step. Moreover, the appendix coll...

  8. Why quantum mechanics?

    International Nuclear Information System (INIS)

    Landsberg, P.T.

    1988-01-01

    It is suggested that an oversight occurred in classical mechanics when time-derivatives of observables were treated on the same footing as the undifferentiated observables. Removal of this oversight points in the direction of quantum mechanics. Additional light is thrown on uncertainty relations and on quantum mechanics, as a possible form of a subtle statistical mechanics, by the formulation of a classical uncertainty relation for a very simple model. The existence of universal motion, i.e., of zero-point energy, is lastly made plausible in terms of a gravitational constant which is time-dependent. By these three considerations an attempt is made to link classical and quantum mechanics together more firmly, thus giving a better understanding of the latter

  9. A Gleason-Type Theorem for Any Dimension Based on a Gambling Formulation of Quantum Mechanics

    Science.gov (United States)

    Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

    2017-07-01

    Based on a gambling formulation of quantum mechanics, we derive a Gleason-type theorem that holds for any dimension n of a quantum system, and in particular for n=2. The theorem states that the only logically consistent probability assignments are exactly the ones that are definable as the trace of the product of a projector and a density matrix operator. In addition, we detail the reason why dispersion-free probabilities are actually not valid, or rational, probabilities for quantum mechanics, and hence should be excluded from consideration.

  10. A mathematical companion to quantum mechanics

    CERN Document Server

    Sternberg, Shlomo

    2019-01-01

    This original 2018 work, based on the author's many years of teaching at Harvard University, examines mathematical methods of value and importance to advanced undergraduates and graduate students studying quantum mechanics. Topics include the Fourier transform, the spectral theorem for bounded self-joint operators, unbounded operators and semigroups, Weyl's theorem, the Rayleigh-Ritz method, one dimensional quantum mechanics, Ruelle's theorem, scattering theory, and many other subjects.

  11. Quantifying Quantum-Mechanical Processes.

    Science.gov (United States)

    Hsieh, Jen-Hsiang; Chen, Shih-Hsuan; Li, Che-Ming

    2017-10-19

    The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of the natural world, from understanding counter-intuitive concepts to the development of wholly quantum-mechanical technology. Here, we show that quantum-mechanical processes can be quantified using a generic classical-process model through which any classical strategies of mimicry can be ruled out. We demonstrate the success of this formalism using fundamental processes postulated in quantum mechanics, the dynamics of open quantum systems, quantum-information processing, the fusion of entangled photon pairs, and the energy transfer in a photosynthetic pigment-protein complex. Since our framework does not depend on any specifics of the states being processed, it reveals a new class of correlations in the hierarchy between entanglement and Einstein-Podolsky-Rosen steering and paves the way for the elaboration of a generic method for quantifying physical processes.

  12. Classical Mechanics as Nonlinear Quantum Mechanics

    International Nuclear Information System (INIS)

    Nikolic, Hrvoje

    2007-01-01

    All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics

  13. Renormalisation in Quantum Mechanics, Quantum Instantons and Quantum Chaos

    OpenAIRE

    Jirari, H.; Kröger, H.; Luo, X. Q.; Moriarty, K. J. M.

    2001-01-01

    We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute quantum instantons and quantum chaos.

  14. Prologue to super quantum mechanics something is rotten in the state of quantum mechanics

    CERN Document Server

    Vaguine, Victor

    2012-01-01

    Since its foundation more than eight decades ago, quantum mechanics has been plagued by enigmas, mysteries and paradoxes and held hostage by quantum positivism. This fact strongly suggests that something is fundamentally wrong with the quantum mechanics paradigm. The best scientific minds, such as Albert Einstein, Louis de Broglie, David Bohm, Richard Feynman and others have spent years of their professional lives attempting to find resolution to the quantum mechanics predicament, with not much success. A shift of the quantum mechanics paradigm toward a deeper physics theory is long overdue.

  15. Lectures in quantum mechanics a two-term course

    CERN Document Server

    Picasso, Luigi E

    2016-01-01

    Based on a series of university lectures on nonrelativistic quantum mechanics, this textbook covers a wide range of topics, from the birth of quantum mechanics to the fine-structure levels of heavy atoms. The author sets out from the crisis in classical physics and explores the seminal ideas of Einstein, Bohr, and de Broglie and their vital importance for the development of quantum mechanics. There follows a bottom-up presentation of the postulates of quantum mechanics through real experiments (such as those of neutron interferometry), with consideration of their most important consequences, including applications in the field of atomic physics. A final chapter is devoted to the paradoxes of quantum mechanics, and particularly those aspects that are still open and hotly debated, to end up with a mention to Bell's theorem and Aspect's experiments. In presenting the principles of quantum mechanics in an inductive way, this book has already proved very popular with students in its Italian language version.It c...

  16. Quantum Mechanics: Fundamentals; Advanced Quantum Mechanics; Mathematical Concepts of Quantum Mechanics

    International Nuclear Information System (INIS)

    Whitaker, A

    2004-01-01

    This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. To commence with general discussion of the new book, the authors recognise that the graduate student of today almost certainly has substantial experience of wave mechanics, and is probably familiar with the Dirac formalism. The new edition has been almost entirely rewritten; even at the level of basic text, it is difficult to trace sentences or paragraphs that have moved unscathed from one edition to the next. As well as the new topics, many of the old ones are discussed in much greater depth, and the general organisation is entirely different. As compared with the steady rise in level of the 1966 edition, the level of this book is fairly consistent throughout, and from the perspective of a beginning graduate student, I would estimate, a little tough. To sum up, Gottfried and Yan's book contains a vast amount of knowledge and understanding. The

  17. Manin's quantum spaces and standard quantum mechanics

    International Nuclear Information System (INIS)

    Floratos, E.G.

    1990-01-01

    Manin's non-commutative coordinate algebra of quantum groups is shown to be identical, for unitary coordinates, with the conventional operator algebras of quantum mechanics. The deformation parameter q is a pure phase for unitary coordinates. When q is a root of unity. Manin's algebra becomes the matrix algebra of quantum mechanics for a discretized and finite phase space. Implications for quantum groups and the associated non-commutative differential calculus of Wess and Zumino are discussed. (orig.)

  18. Bell trajectories for revealing quantum control mechanisms

    International Nuclear Information System (INIS)

    Dennis, Eric; Rabitz, Herschel

    2003-01-01

    The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a ''beable'' formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution onto an ensemble of stochastic trajectories over a classical state space. Detailed mechanism identification is illustrated with a model seven-level system. A general procedure is presented to extract mechanism information directly from closed-loop control experiments. Application to simulated experimental data for the model system proves robust with up to 25% noise

  19. Quantum mechanics

    CERN Document Server

    Ghosh, P K

    2014-01-01

    Quantum mechanics, designed for advanced undergraduate and graduate students of physics, mathematics and chemistry, provides a concise yet self-contained introduction to the formal framework of quantum mechanics, its application to physical problems and the interpretation of the theory. Starting with a review of some of the necessary mathematics, the basic concepts are carefully developed in the text. After building a general formalism, detailed treatment of the standard material - the harmonic oscillator, the hydrogen atom, angular momentum theory, symmetry transformations, approximation methods, identical particle and many-particle systems, and scattering theory - is presented. The concluding chapter discusses the interpretation of quantum mechanics. Some of the important topics discussed in the book are the rigged Hilbert space, deformation quantization, path integrals, coherent states, geometric phases, decoherene, etc. This book is characterized by clarity and coherence of presentation.

  20. Time Dependent Quantum Mechanics

    OpenAIRE

    Morrison, Peter G.

    2012-01-01

    We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic ...

  1. The quantum mechanics solver. How to apply quantum theory to modern physics. 2. ed.

    International Nuclear Information System (INIS)

    Basdevant, J.L.; Dalibard, J.

    2006-01-01

    The Quantum Mechanics Solver uniquely illustrates the application of quantum mechanical concepts to various fields of modern physics. It aims at encouraging the reader to apply quantum mechanics to research problems in fields such as molecular physics, condensed matter physics or laser physics. Advanced undergraduates and graduate students will find a rich and challenging source of material for further exploration. This book consists of a series of problems concerning present-day experimental or theoretical questions on quantum mechanics. All of these problems are based on actual physical examples, even if sometimes the mathematical structure of the models under consideration is simplified intentionally in order to get hold of the physics more rapidly. The new edition features new themes, such as the progress in measuring neutrino oscillations, quantum boxes, the quantum thermometer etc. Secondly, it includes a brief summary on the basics of quantum mechanics and the formalism we use. Finally, the problems under three main themes: Elementary Particles, Nuclei and Atoms; Quantum Entanglement and Measurement; and Complex Systems. (orig.)

  2. Understand quantum mechanics

    International Nuclear Information System (INIS)

    Omnes, R.

    2000-01-01

    The author presents the interpretation of quantum mechanics in a simple and direct way. This book may be considered as a complement of specialized books whose aim is to present the mathematical developments of quantum mechanics. As early as the beginning of quantum theory, Bohr, Heisenberg and Pauli proposed the basis of what is today called the interpretation of Copenhagen. This interpretation is still valid but 2 important discoveries have led to renew some aspects of the interpretation of Copenhagen. The first one was the discovery of the decoherence phenomenon which is responsible for the absence of quantum interferences in the macroscopic world. The second discovery was the achievement of the complete derivation of classical physics from quantum physics, it means that the classical determinism fits in the framework of quantum probabilism. A short summary ends each chapter. (A.C.)

  3. The cellular automaton interpretation of quantum mechanics

    CERN Document Server

    't Hooft, Gerard

    2016-01-01

    This book presents the deterministic view of quantum mechanics developed by Nobel Laureate Gerard 't Hooft. Dissatisfied with the uncomfortable gaps in the way conventional quantum mechanics meshes with the classical world, 't Hooft has revived the old hidden variable ideas, but now in a much more systematic way than usual. In this, quantum mechanics is viewed as a tool rather than a theory. The book presents examples of models that are classical in essence, but can be analysed by the use of quantum techniques, and argues that even the Standard Model, together with gravitational interactions, might be viewed as a quantum mechanical approach to analysing a system that could be classical at its core. He shows how this approach, even though it is based on hidden variables, can be plausibly reconciled with Bell's theorem, and how the usual objections voiced against the idea of ‘superdeterminism' can be overcome, at least in principle. This framework elegantly explains - and automatically cures - the problems of...

  4. Introduction to quantum mechanics

    CERN Document Server

    Phillips, A C

    2003-01-01

    Introduction to Quantum Mechanics is an introduction to the power and elegance of quantum mechanics. Assuming little in the way of prior knowledge, quantum concepts are carefully and precisely presented, and explored through numerous applications and problems. Some of the more challenging aspects that are essential for a modern appreciation of the subject have been included, but are introduced and developed in the simplest way possible.Undergraduates taking a first course on quantum mechanics will find this text an invaluable introduction to the field and help prepare them for more adv

  5. Lectures on Quantum Mechanics

    CERN Document Server

    Dirac, Paul Adrien Maurice

    1964-01-01

    The author of this concise, brilliant series of lectures on mathematical methods in quantum mechanics was one of the shining intellects in the field, winning a Nobel prize in 1933 for his pioneering work in the quantum mechanics of the atom. Beyond that, he developed the transformation theory of quantum mechanics (which made it possible to calculate the statistical distribution of certain variables), was one of the major authors of the quantum theory of radiation, codiscovered the Fermi-Dirac statistics, and predicted the existence of the positron.The four lectures in this book were delivered

  6. Cation solvation with quantum chemical effects modeled by a size-consistent multi-partitioning quantum mechanics/molecular mechanics method.

    Science.gov (United States)

    Watanabe, Hiroshi C; Kubillus, Maximilian; Kubař, Tomáš; Stach, Robert; Mizaikoff, Boris; Ishikita, Hiroshi

    2017-07-21

    In the condensed phase, quantum chemical properties such as many-body effects and intermolecular charge fluctuations are critical determinants of the solvation structure and dynamics. Thus, a quantum mechanical (QM) molecular description is required for both solute and solvent to incorporate these properties. However, it is challenging to conduct molecular dynamics (MD) simulations for condensed systems of sufficient scale when adapting QM potentials. To overcome this problem, we recently developed the size-consistent multi-partitioning (SCMP) quantum mechanics/molecular mechanics (QM/MM) method and realized stable and accurate MD simulations, using the QM potential to a benchmark system. In the present study, as the first application of the SCMP method, we have investigated the structures and dynamics of Na + , K + , and Ca 2+ solutions based on nanosecond-scale sampling, a sampling 100-times longer than that of conventional QM-based samplings. Furthermore, we have evaluated two dynamic properties, the diffusion coefficient and difference spectra, with high statistical certainty. Furthermore the calculation of these properties has not previously been possible within the conventional QM/MM framework. Based on our analysis, we have quantitatively evaluated the quantum chemical solvation effects, which show distinct differences between the cations.

  7. Quantum mechanics the theoretical minimum

    CERN Document Server

    Susskind, Leonard

    2014-01-01

    From the bestselling author of The Theoretical Minimum, an accessible introduction to the math and science of quantum mechanicsQuantum Mechanics is a (second) book for anyone who wants to learn how to think like a physicist. In this follow-up to the bestselling The Theoretical Minimum, physicist Leonard Susskind and data engineer Art Friedman offer a first course in the theory and associated mathematics of the strange world of quantum mechanics. Quantum Mechanics presents Susskind and Friedman’s crystal-clear explanations of the principles of quantum states, uncertainty and time dependence, entanglement, and particle and wave states, among other topics. An accessible but rigorous introduction to a famously difficult topic, Quantum Mechanics provides a tool kit for amateur scientists to learn physics at their own pace.

  8. Relativistic Quantum Mechanics

    International Nuclear Information System (INIS)

    Antoine, J-P

    2004-01-01

    The aim of relativistic quantum mechanics is to describe the finer details of the structure of atoms and molecules, where relativistic effects become nonnegligible. It is a sort of intermediate realm, between the familiar nonrelativistic quantum mechanics and fully relativistic quantum field theory, and thus it lacks the simplicity and elegance of both. Yet it is a necessary tool, mostly for quantum chemists. Pilkuhn's book offers to this audience an up-to-date survey of these methods, which is quite welcome since most previous textbooks are at least ten years old. The point of view of the author is to start immediately in the relativistic domain, following the lead of Maxwell's equations rather than classical mechanics, and thus to treat the nonrelativistic version as an approximation. Thus Chapter 1 takes off from Maxwell's equations (in the noncovariant Coulomb gauge) and gradually derives the basic aspects of Quantum Mechanics in a rather pedestrian way (states and observables, Hilbert space, operators, quantum measurement, scattering,. Chapter 2 starts with the Lorentz transformations, then continues with the Pauli spin equation and the Dirac equation and some of their applications (notably the hydrogen atom). Chapter 3 is entitled 'Quantum fields and particles', but falls short of treating quantum field theory properly: only creation/annihilation operators are considered, for a particle in a box. The emphasis is on two-electron states (the Pauli principle, the Foldy--Wouthuysen elimination of small components of Dirac spinors, Breit projection operators. Chapter 4 is devoted to scattering theory and the description of relativistic bound states. Chapter 5, finally, covers hyperfine interactions and radiative corrections. As we said above, relativistic quantum mechanics is by nature limited in scope and rather inelegant and Pilkuhn's book is no exception. The notation is often heavy (mostly noncovariant) and the mathematical level rather low. The central topic

  9. Quantum mechanics theory and experiment

    CERN Document Server

    Beck, Mark

    2012-01-01

    This textbook presents quantum mechanics at the junior/senior undergraduate level. It is unique in that it describes not only quantum theory, but also presents five laboratories that explore truly modern aspects of quantum mechanics. These laboratories include "proving" that light contains photons, single-photon interference, and tests of local realism. The text begins by presenting the classical theory of polarization, moving on to describe the quantum theory of polarization. Analogies between the two theories minimize conceptual difficulties that students typically have when first presented with quantum mechanics. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Polarization represents a two-dimensional quantum system, so the introduction to quantum mechanics uses two-dimensional state vectors and operators. This allows students to become comfortable with the mat...

  10. Three-space from quantum mechanics

    International Nuclear Information System (INIS)

    Chew, G.F.; Stapp, H.P.

    1988-01-01

    We formulate a discrete quantum-mechanical precursor to spacetime geometry. The objective is to provide the foundation for a quantum mechanics that is rooted exclusively in quantum-mechanical concepts, with all classical features, including the three-dimensional spatial continuum, emerging dynamically

  11. The relation between classical and quantum mechanics

    International Nuclear Information System (INIS)

    Taylor, Peter.

    1984-01-01

    The thesis examines the relationship between classical and quantum mechanics from philosophical, mathematical and physical standpoints. Arguments are presented in favour of 'conjectural realism' in scientific theories, distinguished by explicit contextual structure and empirical testability. The formulations of classical and quantum mechanics, based on a general theory of mechanics is investigated, as well as the mathematical treatments of these subjects. Finally the thesis questions the validity of 'classical limits' and 'quantisations' in intertheoretic reduction. (UK)

  12. The essentials of quantum mechanics

    International Nuclear Information System (INIS)

    Omnes, R.

    2006-09-01

    This book is an introduction to quantum mechanics, the author explains the foundation, interpretation and today limits of this science. The consequences of quantum concepts are reviewed through the lens of recent experimental data. In that way, issues like wave-particle duality, uncertainty principle, decoherence, relationship with classical mechanics or the unicity of reality, issues that were difficult to grasp before, appear now clearer. The book has been divided into 8 chapters: 1) possibility and chance, 2) quantum formalism, 3) fundamental quantum concepts, 4) how to deal with quantum mechanics, 5) decoherence theory, 6) the quantum logic system, 7) the emergence of classical physics, and 8) quantum measurements. (A.C.)

  13. Quantum mechanics of charged particle beam optics

    CERN Document Server

    Khan, Sameen Ahmed

    2018-01-01

    Theory of charged particle beam optics is basic to the design and working of charged particle beam devices from electron microscopes to accelerator machines. Traditionally, the optical elements of the devices are designed and operated based on classical mechanics and classical electromagnetism, and only certain specific quantum mechanical aspects are dealt with separately using quantum theory. This book provides a systematic approach to quantum theory of charged particle beam optics, particularly in the high energy cases such as accelerators or high energy electron microscopy.

  14. The emerging quantum the physics behind quantum mechanics

    CERN Document Server

    Pena, Luis de la; Valdes-Hernandez, Andrea

    2014-01-01

    This monograph presents the latest findings from a long-term research project intended to identify the physics behind Quantum Mechanics. A fundamental theory for quantum mechanics is constructed from first physical principles, revealing quantization as an emergent phenomenon arising from a deeper stochastic process. As such, it offers the vibrant community working on the foundations of quantum mechanics an alternative contribution open to discussion. The book starts with a critical summary of the main conceptual problems that still beset quantum mechanics.  The basic consideration is then introduced that any material system is an open system in permanent contact with the random zero-point radiation field, with which it may reach a state of equilibrium. Working from this basis, a comprehensive and self-consistent theoretical framework is then developed. The pillars of the quantum-mechanical formalism are derived, as well as the radiative corrections of nonrelativistic QED, while revealing the underlying physi...

  15. Supersymmetry and quantum mechanics

    International Nuclear Information System (INIS)

    Cooper, F.; Sukhatme, U.

    1995-01-01

    In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulation of supersymmetric quantum mechanics and discuss many applications. Exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials, shape invariance and operator transformations. Familiar solvable potentials all have the property of shape invariance. We describe new exactly solvable shape invariant potentials which include the recently discovered self-similar potentials as a special case. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Approximation methods are also discussed within the framework of supersymmetric quantum mechanics and in particular it is shown that a supersymmetry inspired WKB approximation is exact for a class of shape invariant potentials. Supersymmetry ideas give particularly nice results for the tunneling rate in a double well potential and for improving large N expansions. We also discuss the problem of a charged Dirac particle in an external magnetic field and other potentials in terms of supersymmetric quantum mechanics. Finally, we discuss structures more general than supersymmetric quantum mechanics such as parasupersymmetric quantum mechanics in which there is a symmetry between a boson and a para-fermion of order p. ((orig.))

  16. Bananaworld quantum mechanics for primates

    CERN Document Server

    Bub, Jeffrey

    2016-01-01

    What on earth do bananas have to do with quantum mechanics? From a modern perspective, quantum mechanics is about strangely counterintuitive correlations between separated systems, which can be exploited in feats like quantum teleportation, unbreakable cryptographic schemes, and computers with enormously enhanced computing power. Schro?dinger coined the term "entanglement" to describe these bizarre correlations. Bananaworld -- an imaginary island with "entangled" bananas -- brings to life the fascinating discoveries of the new field of quantum information without the mathematical machinery of quantum mechanics. The connection with quantum correlations is fully explained in sections written for the non-physicist reader with a serious interest in understanding the mysteries of the quantum world. The result is a subversive but entertaining book that is accessible and interesting to a wide range of readers, with the novel thesis that quantum mechanics is about the structure of information. What we have discovered...

  17. Physics: quantum mechanics

    International Nuclear Information System (INIS)

    Basdevant, J.L.

    1983-01-01

    From important experiment descriptions (sometimes, intentionally simplified), the essential concepts in Quantum Mechanics are first introduced. Wave function notion is described, Schroedinger equation is established, and, after applications rich in physical signification, quantum state and Hilbert space formalism are introduced, which will help to understand many essential phenomena. Then the quantum mechanic general formulation is written and some important consequences are deduced. This formalism is applied to a simple physical problem series (angular momentum, hydrogen atom, etc.) aiming at assimilating the theory operation and its application [fr

  18. Conceptual foundations of quantum mechanics

    International Nuclear Information System (INIS)

    Shimony, A.

    1989-01-01

    Radical innovation in the quantum mechanical framework such as objective indefiniteness, objective chance, objective probability, potentiality, entanglement and quantum nonlocality are discussed and related to the standard formalism. Examples are given which though problematic in classical mechanics are simply explained with these new concepts. Evidence is presented that the conceptual innovations of quantum mechanics cannot be separated from its predictive power. Proposals for solving ''the reduction of the wave packet'' anomaly are presented. Further radical innovations in quantum mechanics are anticipated. (U.K.)

  19. Quantum mechanics. 2. printing (paperback).

    International Nuclear Information System (INIS)

    Lipkin, H.J.

    1986-01-01

    Intended for a first year graduate course in quantum mechanics, this collection of topics can also be considered as a set of self-contained 'monographs for pedestrians' on the Moessbauer effect, many-body quantum mechanics, kaon physics, scattering theory, Feynman diagrams, symmetries and relativistic quantum mechanics. (Auth.)

  20. Quantum mechanics on the personal computer

    International Nuclear Information System (INIS)

    Brandt, S.; Dahmen, H.D.

    1989-01-01

    'Quantum Mechanics on the PC' presents the most up-to-date access to elementary quantum mechanics. Based on the interactive program Interquanta (included on a 5 1/4'' Floppy Disk, MS-DOS) and its extensive 3D colour graphic features, the book guides its readers through computer experiments on - free particles and wave packets - bound states in various potentials - coherent and squeezed states in time-dependent motion - scattering and resonances - analogies in optics - quantized angular momentum - distinguishable and indistinguishable particles - special functions of mathematical physics. The course with a wide variety of more than 250 detailed, class-tested problems provides students with a unique practical experience of complex probability amplitudes, eigenvalues, scattering cross sections and the like. Lecturers and teachers will find excellent, hands-on classroom demonstrations for their quantum mechanics course. (orig.)

  1. Questioning quantum mechanics

    Science.gov (United States)

    Frappier, Mélanie

    2018-03-01

    A century after its inception, quantum mechanics continues to puzzle us with dead-and-alive cats, waves "collapsing" into particles, and "spooky action at a distance." In his first book, What Is Real?, science writer and astrophysicist Adam Becker sets out to explore why the physics community is still arguing today about quantum mechanics's true meaning.

  2. Learning quantum field theory from elementary quantum mechanics

    International Nuclear Information System (INIS)

    Gosdzinsky, P.; Tarrach, R.

    1991-01-01

    The study of the Dirac delta potentials in more than one dimension allows the introduction within the framework of elementary quantum mechanics of many of the basic concepts of modern quantum field theory: regularization, renormalization group, asymptotic freedom, dimensional transmutation, triviality, etc. It is also interesting, by itself, as a nonstandard quantum mechanical problem

  3. Quantum mechanics in chemistry

    CERN Document Server

    Schatz, George C

    2002-01-01

    Intended for graduate and advanced undergraduate students, this text explores quantum mechanical techniques from the viewpoint of chemistry and materials science. Dynamics, symmetry, and formalism are emphasized. An initial review of basic concepts from introductory quantum mechanics is followed by chapters examining symmetry, rotations, and angular momentum addition. Chapter 4 introduces the basic formalism of time-dependent quantum mechanics, emphasizing time-dependent perturbation theory and Fermi's golden rule. Chapter 5 sees this formalism applied to the interaction of radiation and matt

  4. Proceedings of quantum field theory, quantum mechanics, and quantum optics

    International Nuclear Information System (INIS)

    Dodonov, V.V.; Man; ko, V.I.

    1991-01-01

    This book contains papers presented at the XVIII International Colloquium on Group Theoretical Methods in Physics held in Moscow on June 4-9, 1990. Topics covered include; applications of algebraic methods in quantum field theory, quantum mechanics, quantum optics, spectrum generating groups, quantum algebras, symmetries of equations, quantum physics, coherent states, group representations and space groups

  5. Relational quantum mechanics

    International Nuclear Information System (INIS)

    Rovelli, C.

    1996-01-01

    I suggest that the common unease with taking quantum mechanics as a fundamental description of nature (the open-quotes measurement problemclose quotes) could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer-independent time. I suggest that this incorrect notion that generates the unease with quantum mechanics is the notion of open-quotes observer-independent stateclose quotes of a system, or open-quotes observer-independent values of physical quantities.close quotes I reformulate the problem of the open-quotes interpretation of quantum mechanicsclose quotes as the problem of deriving the formalism from a set of simple physical postulates. I consider a reformulation of quantum mechanics in terms of information theory. All systems are assumed to be equivalent, there is no observer-observed distinction, and the theory describes only the information that systems have about each other; nevertheless, the theory is complete

  6. Quantum mechanics II advanced topics

    CERN Document Server

    Rajasekar, S

    2015-01-01

    Quantum Mechanics II: Advanced Topics uses more than a decade of research and the authors’ own teaching experience to expound on some of the more advanced topics and current research in quantum mechanics. A follow-up to the authors introductory book Quantum Mechanics I: The Fundamentals, this book begins with a chapter on quantum field theory, and goes on to present basic principles, key features, and applications. It outlines recent quantum technologies and phenomena, and introduces growing topics of interest in quantum mechanics. The authors describe promising applications that include ghost imaging, detection of weak amplitude objects, entangled two-photon microscopy, detection of small displacements, lithography, metrology, and teleportation of optical images. They also present worked-out examples and provide numerous problems at the end of each chapter.

  7. Quantum Mechanics for Electrical Engineers

    CERN Document Server

    Sullivan, Dennis M

    2011-01-01

    The main topic of this book is quantum mechanics, as the title indicates.  It specifically targets those topics within quantum mechanics that are needed to understand modern semiconductor theory.   It begins with the motivation for quantum mechanics and why classical physics fails when dealing with very small particles and small dimensions.  Two key features make this book different from others on quantum mechanics, even those usually intended for engineers:   First, after a brief introduction, much of the development is through Fourier theory, a topic that is at

  8. Bohmian mechanics. The physics and mathematics of quantum theory

    International Nuclear Information System (INIS)

    Duerr, Detlef; Teufel, Stefan

    2009-01-01

    Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)

  9. Bohmian mechanics. The physics and mathematics of quantum theory

    Energy Technology Data Exchange (ETDEWEB)

    Duerr, Detlef [Muenchen Univ. (Germany). Fakultaet Mathematik; Teufel, Stefan [Tuebingen Univ. (Germany). Mathematisches Inst.

    2009-07-01

    Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)

  10. Quantum mechanical fragment methods based on partitioning atoms or partitioning coordinates.

    Science.gov (United States)

    Wang, Bo; Yang, Ke R; Xu, Xuefei; Isegawa, Miho; Leverentz, Hannah R; Truhlar, Donald G

    2014-09-16

    atoms for capping dangling bonds, and we have shown that they can greatly improve the accuracy. Finally we present a new approach that goes beyond QM/MM by combining the convenience of molecular mechanics with the accuracy of fitting a potential function to electronic structure calculations on a specific system. To make the latter practical for systems with a large number of degrees of freedom, we developed a method to interpolate between local internal-coordinate fits to the potential energy. A key issue for the application to large systems is that rather than assigning the atoms or monomers to fragments, we assign the internal coordinates to reaction, secondary, and tertiary sets. Thus, we make a partition in coordinate space rather than atom space. Fits to the local dependence of the potential energy on tertiary coordinates are arrayed along a preselected reaction coordinate at a sequence of geometries called anchor points; the potential energy function is called an anchor points reactive potential. Electrostatically embedded fragment methods and the anchor points reactive potential, because they are based on treating an entire system by quantum mechanical electronic structure methods but are affordable for large and complex systems, have the potential to open new areas for accurate simulations where combined QM/MM methods are inadequate.

  11. Quantum mechanics from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, C.

    2010-01-01

    Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a 'purity constraint'. Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

  12. Observations of the Ramsauer-Townsend effect in quaternionic quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Sobhani, Hadi [Damghan Branch, Islamic Azad University, Young Researchers and Elite Club, Damghan (Iran, Islamic Republic of); Hassanabadi, Hassan [Shahrood University of Technology, Physics Department (Iran, Islamic Republic of); Chung, Won Sang [Gyeongsang National University, Department of Physics and Research Institute of Natural Science, College of Natural Science, Jinju (Korea, Republic of)

    2017-06-15

    In this article, one of the well-known effects in quantum mechanics is addressed and also the extended form of quantum mechanics which is based on quaternions is presented. In the presence of this version of quantum mechanics the Ramsauer-Townsend effect has been investigated and the existence of this phenomenon is studied according to quaternionic calculations; results are presented by graphs. (orig.)

  13. Supersymmetry in quantum mechanics

    CERN Document Server

    Cooper, Fred; Sukhatme, Uday

    2001-01-01

    This invaluable book provides an elementary description of supersymmetric quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. It gives physicists a fresh outlook and new ways of handling quantum-mechanical problems, and also leads to improved approximation techniques for dealing with potentials of interest in all branches of physics. The algebraic approach to obtaining eigenstates is elegant and important, and all physicists should become familiar with this. The book has been written in such a way that it can be easily appreciated by

  14. Quantum mechanics and the science of measurements

    International Nuclear Information System (INIS)

    Ramsey, N.F.

    1992-01-01

    The accuracies of measurements of almost all fundamental physical constants have increased by factors of about 10,000 during the past 60 years. Although some of the improvements are due to greater care, most are due to new techniques based on quantum mechanics. In popular accounts of quantum mechanics, such great emphases is placed on the Heisenberg Uncertainty Principle that it often appears that the primary effect of quantum mechanics should be to diminish measurement accuracy whereas in most cases it is the validity of quantum mechanics that makes possible the vastly improved measurement accuracies. Seven quantum features that have a profound influence on the science of measurements are: (1) Existence of discrete quantum states of energy W i . (2) Energy conservation in transitions between two states. (3) Electromagnetic radiation of frequency ν is quantized with energy hν per quantum. (4) The identity principle. (5) The Heisenberg Uncertainty Principle. (6) Addition of probability amplitudes (not probabilities) so P=vertical strokeψ 1 +ψ 2 vertical stroke 2 ≠vertical strokeψ 1 vertical stroke 2 +vertical strokeψ 2 vertical stroke 2 . (7) Wave and coherent phase phenomena. Of these seven quantum features, only the Heisenberg Uncertainty Principle limits the accuracy of measurements, and its affect is often negligibly small. The other six features make possible much more accurate measurements of quantum systems than with almost all classical systems and the identity principle provides meaning and significance to highly precise measurements with quantized systems. These effects are discussed and illustrated. (orig.)

  15. Intrinsic resonance representation of quantum mechanics

    DEFF Research Database (Denmark)

    Carioli, M.; Heller, E.J.; Møller, Klaus Braagaard

    1997-01-01

    an optimal representation, based purely on classical mechanics. ''Hidden'' constants of the motion and good actions already known to the classical mechanics are thus incorporated into the basis, leaving the quantum effects to be isolated and included by small matrix diagonalizations. This simplifies...

  16. Analogies between classical statistical mechanics and quantum mechanics

    International Nuclear Information System (INIS)

    Uehara, M.

    1986-01-01

    Some analogies between nonequilibrium classical statistical mechanics and quantum mechanics, at the level of the Liouville equation and at the kinetic level, are commented on. A theorem, related to the Vlasov equation applied to a plasma, is proved. The theorem presents an analogy with Ehrenfest's theorem of quantum mechanics. An analogy between the plasma kinetic theory and Bohm's quantum theory with 'hidden variables' is also shown. (Author) [pt

  17. Improving students' meaningful learning on the predictive nature of quantum mechanics

    Directory of Open Access Journals (Sweden)

    Rodolfo Alves de Carvalho Neto

    2009-03-01

    Full Text Available This paper deals with research about teaching quantum mechanics to 3rd year high school students and their meaningful learning of its predictive aspect; it is based on the Master’s dissertation of one of the authors (CARVALHO NETO, 2006. While teaching quantum mechanics, we emphasized its predictive and essentially probabilistic nature, based on Niels Bohr’s complementarity interpretation (BOHR, 1958. In this context, we have discussed the possibility of predicting measurement results in well-defined experimental contexts, even for individual events. Interviews with students reveal that they have used quantum mechanical ideas, suggesting their meaningful learning of the essentially probabilistic predictions of quantum mechanics.

  18. K-Chains: A New Class of Blockchains and Related Turing Machines Based on Quantum Mechanics

    OpenAIRE

    Hegadekatti, Kartik

    2017-01-01

    Quantum Mechanical principles have brought about a revolution in the way we perceive our world and use technology. One of the possible impacts and usage of Quantum mechanics is in the field of economics. Quantum mechanics can be applied to build a new class of Blockchain systems. This paper explores that possibility. It deals with how Quantum Mechanics can be best implemented to bring into existence a new class of Blockchain systems. These Quantum Blockchains (called K-Chains) will have sever...

  19. Quantum mechanics: why complex Hilbert space?

    Science.gov (United States)

    Cassinelli, G.; Lahti, P.

    2017-10-01

    We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field. This article is part of the themed issue `Second quantum revolution: foundational questions'.

  20. Quantum mechanics with non-negative quantum distribution function

    International Nuclear Information System (INIS)

    Zorin, A.V.; Sevastianov, L.A.

    2010-01-01

    Full text: (author)Among numerous approaches to probabilistic interpretation of the conventional quantum mechanics the most close to the N. Bohr idea of the correspondence principle is the D.I. Blokhintzev - Ya.P. Terletsky approach using the quantum distribution function on the coordinate- momentum space. The detailed investigation of this approach has lead to the correspondence rule of V.V. Kuryshkin. Quantum mechanics of Kuryshkin (QMK) embody the program proposed by Yu.M. Shirokov for unifying classical and quantum mechanics in similar mathematical models. QMK develops and enhances Wigner's proposal concerning the calculation of quantum corrections to classical thermodynamic parameters using a phase distribution function. The main result of QMK is the possibility of description by mean of a positively-valued distribution function. This represents an important step towards a completely statistical model of quantum phenomena, compared with the quasi-probabilistic nature of Wigner distribution. Wigner's model does not permit to perform correctly the classical limit in quantum mechanics as well. On the other hand, QMK has a much more complex structure of operators of observables. One of the unsolved problems of QMK is the absence of a priori rules for establishing of auxiliary functions. Nevertheless, while it is impossible to overcome the complex form of operators, we find it quite possible to derive some methods of filing sets of auxiliary functions

  1. Wigner functions for noncommutative quantum mechanics: A group representation based construction

    Energy Technology Data Exchange (ETDEWEB)

    Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com [Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada)

    2015-12-15

    This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.

  2. Relativity, Symmetry, and the Structure of Quantum Theory, Volume 2; Point form relativistic quantum mechanics

    Science.gov (United States)

    Klink, William H.; Schweiger, Wolfgang

    2018-03-01

    This book covers relativistic quantum theory from the point of view of a particle theory, based on the irreducible representations of the Poincaré group, the group that expresses the symmetry of Einstein relativity. There are several ways of formulating such a theory; this book develops what is called relativistic point form quantum mechanics, which, unlike quantum field theory, deals with a fixed number of particles in a relativistically invariant way. A chapter is devoted to applications of point form quantum mechanics to nuclear physics.

  3. Development and validation of an achievement test in introductory quantum mechanics: The Quantum Mechanics Visualization Instrument (QMVI)

    Science.gov (United States)

    Cataloglu, Erdat

    The purpose of this study was to construct a valid and reliable multiple-choice achievement test to assess students' understanding of core concepts of introductory quantum mechanics. Development of the Quantum Mechanics Visualization Instrument (QMVI) occurred across four successive semesters in 1999--2001. During this time 213 undergraduate and graduate students attending the Pennsylvania State University (PSU) at University Park and Arizona State University (ASU) participated in this development and validation study. Participating students were enrolled in four distinct groups of courses: Modern Physics, Undergraduate Quantum Mechanics, Graduate Quantum Mechanics, and Chemistry Quantum Mechanics. Expert panels of professors of physics experienced in teaching quantum mechanics courses and graduate students in physics and science education established the core content and assisted in the validating of successive versions of the 24-question QMVI. Instrument development was guided by procedures outlined in the Standards for Educational and Psychological Testing (AERA-APA-NCME, 1999). Data gathered in this study provided information used in the development of successive versions of the QMVI. Data gathered in the final phase of administration of the QMVI also provided evidence that the intended score interpretation of the QMVI achievement test is valid and reliable. A moderate positive correlation coefficient of 0.49 was observed between the students' QMVI scores and their confidence levels. Analyses of variance indicated that students' scores in Graduate Quantum Mechanics and Undergraduate Quantum Mechanics courses were significantly higher than the mean scores of students in Modern Physics and Chemistry Quantum Mechanics courses (p important factor for students in acquiring a successful understanding of quantum mechanics.

  4. A textbook of quantum mechanics

    International Nuclear Information System (INIS)

    Mathews, P.M.; Venkatesan, K.

    1977-01-01

    After briefly surveying the inadequacy of the classical ideas and elementary older quantum theory, the ideas of wave mechanics, the postulates of quantum mechanics, exactly soluble problems, approximation techniques, scattering theory, angular momentum, time dependent problems and the basic ideas of relativistic quantum mechanics are discussed. The book is meant for the Master of Science degree course students of Indian Universities. (M.G.B.)

  5. Fundamentals of Quantum Mechanics

    Science.gov (United States)

    Tang, C. L.

    2005-06-01

    Quantum mechanics has evolved from a subject of study in pure physics to one with a wide range of applications in many diverse fields. The basic concepts of quantum mechanics are explained in this book in a concise and easy-to-read manner emphasising applications in solid state electronics and modern optics. Following a logical sequence, the book is focused on the key ideas and is conceptually and mathematically self-contained. The fundamental principles of quantum mechanics are illustrated by showing their application to systems such as the hydrogen atom, multi-electron ions and atoms, the formation of simple organic molecules and crystalline solids of practical importance. It leads on from these basic concepts to discuss some of the most important applications in modern semiconductor electronics and optics. Containing many homework problems and worked examples, the book is suitable for senior-level undergraduate and graduate level students in electrical engineering, materials science and applied physics. Clear exposition of quantum mechanics written in a concise and accessible style Precise physical interpretation of the mathematical foundations of quantum mechanics Illustrates the important concepts and results by reference to real-world examples in electronics and optoelectronics Contains homeworks and worked examples, with solutions available for instructors

  6. The Misapplication of Probability Theory in Quantum Mechanics

    Science.gov (United States)

    Racicot, Ronald

    2014-03-01

    This article is a revision of two papers submitted to the APS in the past two and a half years. In these papers, arguments and proofs are summarized for the following: (1) The wrong conclusion by EPR that Quantum Mechanics is incomplete, perhaps requiring the addition of ``hidden variables'' for completion. Theorems that assume such ``hidden variables,'' such as Bell's theorem, are also wrong. (2) Quantum entanglement is not a realizable physical phenomenon and is based entirely on assuming a probability superposition model for quantum spin. Such a model directly violates conservation of angular momentum. (3) Simultaneous multiple-paths followed by a quantum particle traveling through space also cannot possibly exist. Besides violating Noether's theorem, the multiple-paths theory is based solely on probability calculations. Probability calculations by themselves cannot possibly represent simultaneous physically real events. None of the reviews of the submitted papers actually refuted the arguments and evidence that was presented. These analyses should therefore be carefully evaluated since the conclusions reached have such important impact in quantum mechanics and quantum information theory.

  7. Locality and quantum mechanics.

    Science.gov (United States)

    Unruh, W G

    2018-07-13

    It is argued that it is best not to think of quantum mechanics as non-local, but rather that it is non-realistic.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

  8. Problems in quantum mechanics

    CERN Document Server

    Goldman, Iosif Ilich; Geilikman, B T

    2006-01-01

    This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.

  9. Charge transport model in nanodielectric composites based on quantum tunneling mechanism and dual-level traps

    Energy Technology Data Exchange (ETDEWEB)

    Li, Guochang; Chen, George, E-mail: gc@ecs.soton.ac.uk, E-mail: sli@mail.xjtu.edu.cn [State Key Laboratory of Electrical Insulation and Power Equipment, Xi' an Jiaotong University, Xi' an 710049 (China); School of Electronic and Computer Science, University of Southampton, Southampton SO17 1BJ (United Kingdom); Li, Shengtao, E-mail: gc@ecs.soton.ac.uk, E-mail: sli@mail.xjtu.edu.cn [State Key Laboratory of Electrical Insulation and Power Equipment, Xi' an Jiaotong University, Xi' an 710049 (China)

    2016-08-08

    Charge transport properties in nanodielectrics present different tendencies for different loading concentrations. The exact mechanisms that are responsible for charge transport in nanodielectrics are not detailed, especially for high loading concentration. A charge transport model in nanodielectrics has been proposed based on quantum tunneling mechanism and dual-level traps. In the model, the thermally assisted hopping (TAH) process for the shallow traps and the tunnelling process for the deep traps are considered. For different loading concentrations, the dominant charge transport mechanisms are different. The quantum tunneling mechanism plays a major role in determining the charge conduction in nanodielectrics with high loading concentrations. While for low loading concentrations, the thermal hopping mechanism will dominate the charge conduction process. The model can explain the observed conductivity property in nanodielectrics with different loading concentrations.

  10. Quantum mechanics and Bell's inequalities

    International Nuclear Information System (INIS)

    Jones, R.T.; Adelberger, E.G.

    1994-01-01

    Santos argues that, if one interprets probabilities as ratios of detected events to copies of the physical system initially prepared, the quantum mechanical predictions for the classic tests of Bell's inequalities do not violate the inequalities. Furthermore, he suggests that quantum mechanical states which do violate the inequalities are not physically realizable. We discuss a physically realizable experiment, meeting his requirements, where quantum mechanics does violate the inequalities

  11. Categorization of Quantum Mechanics Problems by Professors and Students

    Science.gov (United States)

    Lin, Shih-Yin; Singh, Chandralekha

    2010-01-01

    We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…

  12. Quantum mechanics: why complex Hilbert space?

    Science.gov (United States)

    Cassinelli, G; Lahti, P

    2017-11-13

    We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

  13. DEMYSTIFYING QUANTUM MECHANICS: Will there be hints from LHC?

    CERN Multimedia

    CERN. Geneva

    2007-01-01

    All modern theories for particles, forces and even space-time itself, use the framework provided by quantum mechanics. The Standard Model is a quantized field theory. Even superstring theory is based on quantum mechanics. There is something odd about quantum mechanics: it brilliantly allows us to predict the outcome of experiments, yet it gives confusing statements about what really is going on inside particles and fields. Suppose we would be asking for a theory that allows us to describe what actually happens in less ambiguous terms, without destroying the magnificent successes of quantum mechanics, would this help us to answer some of the great mysteries of theoretical elementary particle physics?Organiser(s): L. Alvarez-Gaume / PH-THNote: * Tea & coffee will be served at 16:00.

  14. Nilpotent Quantum Mechanics: Analogs and Applications

    Directory of Open Access Journals (Sweden)

    Peter Marcer

    2017-07-01

    Full Text Available The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state and its environment (vacuum are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This zero square-root construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on “The ‘Logic’ of Self-Organizing Systems” [1], in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantum mechanics, will apply.

  15. Quantum mechanics by walking 1. Foundations

    International Nuclear Information System (INIS)

    Pade, Jochen

    2012-01-01

    Quantum mechanics by walking introduces to the foundations of non-relativistic quantum mechanics. This book applies to studyings of teaching physics as well as all studyings of physics, who look for an appropriate, easy, fresh, and modern approach to the field. In the present first volume the essential principles of quantum mechanics are worked out. in order to be able to develop their mathematical formulation as fastly and clearly as possible, systematically between wave mechanics and algebraic presentation is changed. Beside themes, which are traditionally in textbooks of quantum mechanics, extensively actual aspects like interaction-free quantum measurement, neutrino oscillations, or quantum cryptography are considered as well as fundamental problems and epistemological questions discussed, as they occur in connection with the measurement process. The list of the postulates of quantum mechanics closes this volume; they form the framework for the extensions and applications, which are discussed in the second volume. The required mathematical aids are introduced step by step. In the appendix the most important mathematical tools are compactly collected, so that supplementing literature can be far reachingly abandoned. Furthermore in the appendix supplementing themes are deepened as for instance the Quantum Zeno effect or delayed-choice experiments.

  16. Analytical mechanics for relativity and quantum mechanics

    CERN Document Server

    Johns, Oliver Davis

    2011-01-01

    Analytical Mechanics for Relativity and Quantum Mechanics is an innovative and mathematically sound treatment of the foundations of analytical mechanics and the relation of classical mechanics to relativity and quantum theory. It is intended for use at the introductory graduate level. A distinguishing feature of the book is its integration of special relativity into teaching of classical mechanics. After a thorough review of the traditional theory, Part II of the book introduces extended Lagrangian and Hamiltonian methods that treat time as a transformable coordinate rather than the fixed parameter of Newtonian physics. Advanced topics such as covariant Langrangians and Hamiltonians, canonical transformations, and Hamilton-Jacobi methods are simplified by the use of this extended theory. And the definition of canonical transformation no longer excludes the Lorenz transformation of special relativity. This is also a book for those who study analytical mechanics to prepare for a critical exploration of quantum...

  17. From wave mechanics to quantum chemistry

    International Nuclear Information System (INIS)

    Daudel, R.

    1996-01-01

    The origin of wave mechanics, which is now called quantum mechanics, is evoked. The main stages of the birth of quantum chemistry are related as resulting from the application of quantum mechanics to the study of molecular properties and chemical reactions. (author). 14 refs

  18. Quantum mechanics and the physical reality concept

    International Nuclear Information System (INIS)

    von Borzeszkowski, H.H.; Wahsner, R.

    1988-01-01

    The difference between the measurement bases of classical and quantum mechanics is often interpreted as a loss of reality arising in quantum mechanics. In this paper it is shown that this apparent loss occurs only if one believes that refined everyday experience determines the Euclidean space as the real space, instead of considering this space, both in classical and quantum mechanics, as a theoretical construction needed for measurement and representing one part of a dualistic space conception. From this point of view, Einstein's program of a unified field theory can be interpreted as the attempt to find a physical theory that is less dualistic. However, if one regards this dualism as resulting from the requirements of measurements, one can hope for a weakening of the dualism but not expect to remove it completely

  19. Quantum mechanics and quantum information a guide through the quantum world

    CERN Document Server

    Fayngold, Moses

    2013-01-01

    Alongside a thorough definition of the basic concepts and their interrelations, backed by numerous examples, this textbook features a rare discussion of the quantum information theory. It also deals with other important topics hardly found in the literature, including the Robertson-Schrodinger-relation, angle and angular momentum uncertainties, interaction-free measurements, and the limitations of the no-cloning theorem With its interpretations of quantum mechanics and its discussions of quantum computing, this book is poised to become the standard textbook for advanced undergraduate and beginning graduate quantum mechanics courses and as an essential reference for physics students and physics professionals.

  20. Geometric Aspects of Quantum Mechanics and Quantum Entanglement

    International Nuclear Information System (INIS)

    Chruscinski, Dariusz

    2006-01-01

    It is shown that the standard non-relativistic Quantum Mechanics gives rise to elegant and rich geometrical structures. The space of quantum states is endowed with nontrivial Fubini-Study metric which is responsible for the 'peculiarities' of the quantum world. We show that there is also intricate connection between geometrical structures and quantum entanglement

  1. Modern logic and quantum mechanics

    International Nuclear Information System (INIS)

    Garden, R.W.

    1984-01-01

    The book applies the methods of modern logic and probabilities to ''interpreting'' quantum mechanics. The subject is described and discussed under the chapter headings: classical and quantum mechanics, modern logic, the propositional logic of mechanics, states and measurement in mechanics, the traditional analysis of probabilities, the probabilities of mechanics and the model logic of predictions. (U.K.)

  2. Bohmian mechanics, open quantum systems and continuous measurements

    CERN Document Server

    Nassar, Antonio B

    2017-01-01

    This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from th...

  3. How one can construct a consistent relativistic quantum mechanics on the base of a relativistic wave equation

    Energy Technology Data Exchange (ETDEWEB)

    Gavrilov, S.P. [Universidade Federal de Sergipe (UFS), Aracaju, SE (Brazil); Gitman, D.M. [Sao Paulo Univ. (USP), SP (Brazil). Inst. de Fisica

    2000-07-01

    Full text follows: There is a common opinion that the construction of a consistent relativistic quantum mechanics on the base of a relativistic wave equation meets well-known difficulties related to the existence of infinite number of negative energy levels, to the existence of negative vector norms, and so on, which may be only solved in a second-quantized theory, see, for example, two basic papers devoted to the problem L.Foldy, S.Wouthuysen, Phys. Rep.78 (1950) 29; H.Feshbach, F.Villars, Rev. Mod. Phys. 30 (1958) 24, whose arguments are repeated in all handbooks in relativistic quantum theory. Even Dirac trying to solve the problem had turned last years to infinite-component relativistic wave equations, see P.A.M. Dirac, Proc. R. Soc. London, A328 (1972) 1. We believe that a consistent relativistic quantum mechanics may be constructed on the base of an extended (charge symmetric) equation, which unite both a relativistic wave equation for a particle and for an antiparticle. We present explicitly the corresponding construction, see for details hep-th/0003112. We support such a construction by two demonstrations: first, in course of a careful canonical quantization of the corresponding classical action of a relativistic particle we arrive just to such a consistent quantum mechanics; second, we demonstrate that a reduction of the QFT of a corresponding field (scalar, spinor, etc.) to one-particle sector, if such a reduction may be done, present namely this quantum mechanics. (author)

  4. Quantum mechanics a fundamental approach

    CERN Document Server

    Wan, K Kong

    2018-01-01

    The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning. This makes it difficult to appreciate the mathematical formalism and hampers the understanding of quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. Quantum mechanics is presented in six groups of postulates. A chapter is devoted to each group of postulates with a detailed discussion. Systems with superselection rules, and some conceptual issues such as quantum paradoxes and measurement, are also discussed. The book conc...

  5. Logical foundation of quantum mechanics

    International Nuclear Information System (INIS)

    Stachow, E.W.

    1980-01-01

    The subject of this article is the reconstruction of quantum mechanics on the basis of a formal language of quantum mechanical propositions. During recent years, research in the foundations of the language of science has given rise to a dialogic semantics that is adequate in the case of a formal language for quantum physics. The system of sequential logic which is comprised by the language is more general than classical logic; it includes the classical system as a special case. Although the system of sequential logic can be founded without reference to the empirical content of quantum physical propositions, it establishes an essential part of the structure of the mathematical formalism used in quantum mechanics. It is the purpose of this paper to demonstrate the connection between the formal language of quantum physics and its representation by mathematical structures in a self-contained way. (author)

  6. Bell's theorem and quantum mechanics

    Science.gov (United States)

    Rosen, Nathan

    1994-02-01

    Bell showed that assuming locality leads to a disagreement with quantum mechanics. Here the nature of the nonlocality that follows from quantum mechanics is investigated. Note by the Editor—Readers will recognize Professor Rosen, author of this paper, as one of the co-authors of the famous EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen, ``Can Quantum-Mechanical Description of Physical Reality be considered Complete?'', Phys. Rev. 47, 770-780 (1935). Robert H. Romer, Editor

  7. Nonlocal quantum field theory and stochastic quantum mechanics

    International Nuclear Information System (INIS)

    Namsrai, K.

    1986-01-01

    This volume presents a systematic development of the implications to both quantum mechanics and quantum field theory of the hypothesis of a stochastic structure of space-time. Some applications to elementary particle physics are also considered. Part 1 is concerned with nonlocal quantum field theory and, among other topics, deals with quantized fields, electromagnetic and weak processes, the Schroedinger equation, and functional methods and their applications. Part 2 presents an introduction to stochastic mechanics and many specific problems of interest are discussed. (Auth.)

  8. Quantum ballistic evolution in quantum mechanics: Application to quantum computers

    International Nuclear Information System (INIS)

    Benioff, P.

    1996-01-01

    Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single-step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators T is investigated here. The main limitation of this paper is to processes which evolve quantum ballistically, i.e., motion restricted to a collection of nonintersecting or distinct paths on an arbitrary basis. The main goal of this paper is proof of a theorem which gives necessary and sufficient conditions that T must satisfy so that there exists a Hamiltonian description of quantum ballistic evolution for the process, namely, that T is a partial isometry and is orthogonality preserving and stable on some basis. Simple examples of quantum ballistic evolution for quantum Turing machines with one and with more than one type of elementary step are discussed. It is seen that for nondeterministic machines the basis set can be quite complex with much entanglement present. It is also proven that, given a step operator T for an arbitrary deterministic quantum Turing machine, it is decidable if T is stable and orthogonality preserving, and if quantum ballistic evolution is possible. The proof fails if T is a step operator for a nondeterministic machine. It is an open question if such a decision procedure exists for nondeterministic machines. This problem does not occur in classical mechanics. Also the definition of quantum Turing machines used here is compared with that used by other authors. copyright 1996 The American Physical Society

  9. Random path formulation of nonrelativistic quantum mechanics

    International Nuclear Information System (INIS)

    Roncadelli, M.

    1993-01-01

    Quantum amplitudes satisfy (almost) the same calculus that probabilities obey in the theory of classical stochastic diffusion processes. As a consequence of this structural analogy, a new formulation of (nonrelativistic) quantum mechanics naturally arises as the quantum counterpart of the Langevin description of (classical) stochastic diffusion processes. Quantum fluctuations are simulated here by a Fresnel white noise (FWN), which is a (real) white noise with imaginary diffusion constant, whose functional (pseudo) measure yields the amplitude distribution for its configurations. Central to this approach is the idea that classical dynamical trajectories in configuration space are perturbed by the FWN. Hence, a single (arbitrary) classical dynamical path gets replaced by a family of quantum random paths (QRPs) - one for each FWN sample - all originating from the same space-time point (x', t'). The QRPs are the basic objects of the present formulation and are given by a Langevin equation with the FWN, whose drift is controlled by a (arbitrary) solution to the classical Hamilton-Jacobi equation. So, our approach is manifestly based on classical dynamics. Now, a transition amplitude is associated with each QRP: it gives the amplitude that a particle starting from (x', t') will reach (x'', t'') by travelling just along the considered QRP. The quantum mechanical propagator (x'', t'' modul x', t') then emerges as the FWN average of the transition amplitude along a QRP. Thus, quantum mechanics looks like classical mechanics as perturbed by the FWN. The general structure of this formulation is discussed in detail, along with some practical and conceptual implications. (author). 14 refs

  10. Emergent quantum mechanics without wavefunctions

    Science.gov (United States)

    Mesa Pascasio, J.; Fussy, S.; Schwabl, H.; Grössing, G.

    2016-03-01

    We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques.

  11. Supersymmetric symplectic quantum mechanics

    Science.gov (United States)

    de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

    2018-02-01

    Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

  12. Search for violations of quantum mechanics

    International Nuclear Information System (INIS)

    Ellis, J.; Hagelin, J.S.; Nanopoulos, D.V.; Srednicki, M.

    1984-01-01

    The treatment of quantum effects in gravitational fields indicates that pure states may evolve into mixed states, and Hawking has proposed modification of the axioms of field theory which incorporate the corresponding violation of quantum mechanics. In this paper we propose a modified hamiltonian equation of motion for density matrices and use it to interpret upper bounds on the violation of quantum mechanics in different phenomenological situations. We apply our formalism to the K 0 -anti K 0 system and to long baseline neutron interferometry experiments. In both cases we find upper bounds of about 2x10 -21 GeV on contributions to the single particle 'hamiltonian' which violate quantum mechanical coherence. We discuss how these limits might be improved in the future, and consider the relative significance of other successful tests of quantum mechanics. An appendix contains model estimates of the magnitude of effects violating quantum mechanics. (orig.)

  13. Emerging interpretations of quantum mechanics and recent progress in quantum measurement

    International Nuclear Information System (INIS)

    Clarke, M L

    2014-01-01

    The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism). (paper)

  14. Review of student difficulties in upper-level quantum mechanics

    Directory of Open Access Journals (Sweden)

    Chandralekha Singh

    2015-09-01

    Full Text Available [This paper is part of the Focused Collection on Upper Division Physics Courses.] Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical mechanics and quantum mechanics are very different. Here, we review research on student reasoning difficulties in learning upper-level quantum mechanics and research on students’ problem-solving and metacognitive skills in these courses. Some of these studies were multiuniversity investigations. The investigations suggest that there is large diversity in student performance in upper-level quantum mechanics regardless of the university, textbook, or instructor, and many students in these courses have not acquired a functional understanding of the fundamental concepts. The nature of reasoning difficulties in learning quantum mechanics is analogous to reasoning difficulties found via research in introductory physics courses. The reasoning difficulties were often due to overgeneralizations of concepts learned in one context to another context where they are not directly applicable. Reasoning difficulties in distinguishing between closely related concepts and in making sense of the formalism of quantum mechanics were common. We conclude with a brief summary of the research-based approaches that take advantage of research on student difficulties in order to improve teaching and learning of quantum mechanics.

  15. Fundamentals of quantum mechanics

    CERN Document Server

    House, J E

    2017-01-01

    Fundamentals of Quantum Mechanics, Third Edition is a clear and detailed introduction to quantum mechanics and its applications in chemistry and physics. All required math is clearly explained, including intermediate steps in derivations, and concise review of the math is included in the text at appropriate points. Most of the elementary quantum mechanical models-including particles in boxes, rigid rotor, harmonic oscillator, barrier penetration, hydrogen atom-are clearly and completely presented. Applications of these models to selected “real world” topics are also included. This new edition includes many new topics such as band theory and heat capacity of solids, spectroscopy of molecules and complexes (including applications to ligand field theory), and small molecules of astrophysical interest.

  16. Tunneling time in space fractional quantum mechanics

    Science.gov (United States)

    Hasan, Mohammad; Mandal, Bhabani Prasad

    2018-02-01

    We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for b → ∞ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.

  17. Combined quantum and molecular mechanics (QM/MM).

    Science.gov (United States)

    Friesner, Richard A

    2004-12-01

    We describe the current state of the art of mixed quantum mechanics/molecular mechanics (QM/MM) methodology, with a particular focus on modeling of enzymatic reactions. Over the past decade, the effectiveness of these methods has increased dramatically, based on improved quantum chemical methods, advances in the description of the QM/MM interface, and reductions in the cost/performance of computing hardware. Two examples of pharmaceutically relevant applications, cytochrome P450 and class C β-lactamase, are presented.: © 2004 Elsevier Ltd . All rights reserved.

  18. A derivation of the classical limit of quantum mechanics and quantum electrodynamics

    International Nuclear Information System (INIS)

    Ajanapon, P.

    1985-01-01

    Instead of regarding the classical limit as the h → 0, an alternative view based on the physical interpretation of the elements of the density matrix is proposed. According to this alternative view, taking the classical limit corresponds to taking the diagonal elements and ignoring the off-diagonal elements of the density matrix. As illustrations of this alternative approach, the classical limits of quantum mechanics and quantum electrodynamics are derived. The derivation is carried out in two stages. First, the statistical classical limit is derived. Then with an appropriate initial condition, the deterministic classical limit is obtained. In the case of quantum mechanics, it is found that the classical limit of Schroedinger's wave mechanics is at best statistical, i.e., Schroedinger's wave mechanics does not reduce to deterministic (Hamilton's or Newton's) classical mechanics. In order to obtain the latter, it is necessary to start out initially with a mixture at the level of statistical quantum mechanics. The derivation hinges on the use of the Feynman path integral rigorously defined with the aid of nonstandard analysis. Nonstandard analysis is also applied to extend the method to the case of quantum electrodynamics. The fundamental decoupling problem arising form the use of Grassmann variables is circumvented by the use of c-number electron fields, but antisymmetrically tagged. The basic classical (deterministic) field equations are obtained in the classical limit with appropriate initial conditions. The result raises the question as to what the corresponding classical field equations obtained in the classical limit from the renormalized Lagrangian containing infinite counterterms really mean

  19. Protein Structure Validation and Refinement Using Chemical Shifts Derived from Quantum Mechanics

    DEFF Research Database (Denmark)

    Bratholm, Lars Andersen

    to within 3 A. Furthermore, a fast quantum mechanics based chemical shift predictor was developed together with methodology for using chemical shifts in structure simulations. The developed predictor was used for renement of several protein structures and for reducing the computational cost of quantum...... mechanics / molecular mechanics (QM/MM) computations of chemical shieldings. Several improvements to the predictor is ongoing, where among other things, kernel based machine learning techniques have successfully been used to improve the quantum mechanical level of theory used in the predictions....

  20. Multiple-event probability in general-relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Hellmann, Frank; Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo

    2007-01-01

    We discuss the definition of quantum probability in the context of 'timeless' general-relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multievent probability. In conventional quantum mechanics this can be obtained by means of the 'wave function collapse' algorithm. We first point out certain difficulties of some natural definitions of multievent probability, including the conditional probability widely considered in the literature. We then observe that multievent probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum/classical boundary, one can always trade a sequence of noncommuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the wave function collapse algorithm can nevertheless be recovered. The discussion also bears on the nature of the quantum collapse

  1. A modern approach to quantum mechanics

    CERN Document Server

    Townsend, John S

    2012-01-01

    Using an innovative approach that students find both accessible and exciting, A Modern Approach to Quantum Mechanics, Second Edition lays out the foundations of quantum mechanics through the physics of intrinsic spin. Written to serve as the primary textbook for an upper-division course in quantum mechanics, Townsend's text gives professors and students a refreshing alternative to the old style of teaching, by allowing the basic physics of spin systems to drive the introduction of concepts such as Dirac notation, operators, eigenstates and eigenvalues, time evolution in quantum mechanics, and entanglement. Chapters 6 through 10 cover the more traditional subjects in wave mechanics-the Schrodinger equation in position space, the harmonic oscillator, orbital angular momentum, and central potentials-but they are motivated by the foundations developed in the earlier chapters. Students using this text will perceive wave mechanics as an important aspect of quantum mechanics, but not necessarily the core of the subj...

  2. Quantum mechanical features of optically pumped CW FIR lasers

    Science.gov (United States)

    Seligson, D.; Leite, J. R. R.; Sanchez, A.; Feld, M. S.; Ducloy, M.

    1977-01-01

    Quantum mechanical predictions for the gain of an optically pumped CW FIR laser are presented for cases in which one or both of the pump and FIR transitions are pressure or Doppler broadened. The results are compared to those based on the rate equation model. Some of the quantum mechanical predictions are verified in CH3OH.

  3. Pseudo-Hermitian Representation of Quantum Mechanics

    International Nuclear Information System (INIS)

    Mustafazade, A.

    2008-01-01

    I will outline a formulation of quantum mechanics in which the inner product on the Hilbert space of a quantum system is treated as a degree of freedom. I will outline some of the basic mathematical and conceptual features of the resulting theory and discuss some of its applications. In particular, I will present a quantum mechanical analogue of Einstein's field equations that links the inner product of the Hilbert space and the Hamiltonian of the system and discuss how the resulting theory can be used to address a variety of problems in classical electrodynamics, relativistic quantum mechanics, and quantum computation

  4. Lectures on quantum mechanics

    CERN Document Server

    Weinberg, Steven

    2013-01-01

    Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a concise introduction to modern quantum mechanics. Ideally suited to a one-year graduate course, this textbook is also a useful reference for researchers. Readers are introduced to the subject through a review of the history of quantum mechanics and an account of classic solutions of the Schrödinger equation, before quantum mechanics is developed in a modern Hilbert space approach. The textbook covers many topics not often found in other books on the subject, including alternatives to the Copenhagen interpretation, Bloch waves and band structure, the Wigner–Eckart theorem, magic numbers, isospin symmetry, the Dirac theory of constrained canonical systems, general scattering theory, the optical theorem, the 'in-in' formalism, the Berry phase, Landau levels, entanglement and quantum computing. Problems are included at the ends of chapters, with solutions available for instructors at www.cam...

  5. Quantum Mechanical Earth: Where Orbitals Become Orbits

    Science.gov (United States)

    Keeports, David

    2012-01-01

    Macroscopic objects, although quantum mechanical by nature, conform to Newtonian mechanics under normal observation. According to the quantum mechanical correspondence principle, quantum behavior is indistinguishable from classical behavior in the limit of very large quantum numbers. The purpose of this paper is to provide an example of the…

  6. Quantum mechanics in Hilbert space

    CERN Document Server

    Prugovecki, Eduard

    1981-01-01

    A critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate levels. Its readable and self-contained form is accessible even to students without an extensive mathematical background. Applications of basic theorems to quantum mechanics make it of particular interest to mathematicians working in functional analysis and related areas.This text features the rigorous proofs of all the main functional-analytic statements encountered in books on quantum mechanics. It fills the

  7. Measurement theory in quantum mechanics

    International Nuclear Information System (INIS)

    Klein, G.

    1980-01-01

    It is assumed that consciousness, memory and liberty (within the limits of the quantum mechanics indeterminism) are fundamental properties of elementary particles. Then, using this assumption it is shown how measurements and observers may be introduced in a natural way in the quantum mechanics theory. There are no longer fundamental differences between macroscopic and microscopic objects, between classical and quantum objects, between observer and object. Thus, discrepancies and paradoxes have disappeared from the conventional quantum mechanics theory. One consequence of the cumulative memory of the particles is that the sum of negentropy plus information is a constant. Using this theory it is also possible to explain the 'paranormal' phenomena and what is their difference from the 'normal' ones [fr

  8. Emergent quantum mechanics without wavefunctions

    International Nuclear Information System (INIS)

    Pascasio, J Mesa; Fussy, S; Schwabl, H; Grössing, G

    2016-01-01

    We present our model of an Emergent Quantum Mechanics which can be characterized by “realism without pre-determination”. This is illustrated by our analytic description and corresponding computer simulations of Bohmian-like “surreal” trajectories, which are obtained classically, i.e. without the use of any quantum mechanical tool such as wavefunctions. However, these trajectories do not necessarily represent ontological paths of particles but rather mappings of the probability density flux in a hydrodynamical sense. Modelling emergent quantum mechanics in a high-low intesity double slit scenario gives rise to the “quantum sweeper effect” with a characteristic intensity pattern. This phenomenon should be experimentally testable via weak measurement techniques. (paper)

  9. Randomness and locality in quantum mechanics

    International Nuclear Information System (INIS)

    Bub, J.

    1976-01-01

    This paper considers the problem of representing the statistical states of a quantum mechanical system by measures on a classical probability space. The Kochen and Specker theorem proves the impossibility of embedding the possibility structure of a quantum mechanical system into a Boolean algebra. It is shown that a hidden variable theory involves a Boolean representation which is not an embedding, and that such a representation cannot recover the quantum statistics for sequential probabilities without introducing a randomization process for the hidden variables which is assumed to apply only on measurement. It is suggested that the relation of incompatability is to be understood as a type of stochastic independence, and that the indeterminism of a quantum mechanical system is engendered by the existence of independent families of properties. Thus, the statistical relations reflect the possibility structure of the system: the probabilities are logical. The hidden variable thesis is influenced by the Copenhagen interpretation of quantum mechanics, i.e. by some version of the disturbance theory of measurement. Hence, the significance of the representation problem is missed, and the completeness of quantum mechanics is seen to turn on the possibility of recovering the quantum statistics by a hidden variable scheme which satisfies certain physically motivated conditions, such as locality. Bell's proof that no local hidden variable theory can reproduce the statistical relations of quantum mechanics is considered. (Auth.)

  10. On quantum gravity and the many-worlds interpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Smolin, L.

    1984-01-01

    The paper examines the interpretation of quantum mechanics and the quantum theory of gravity. Foundational problems in quantum gravity; the many-worlds interpretation of quantum mechanics; the role of observation in the many-worlds and in the minimal relative state interpretations; and advantages of the many-worlds interpretation; are all discussed. (U.K.)

  11. Maximally causal quantum mechanics

    International Nuclear Information System (INIS)

    Roy, S.M.

    1998-01-01

    We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics. (author)

  12. QUANTUM MECHANICS. Quantum squeezing of motion in a mechanical resonator.

    Science.gov (United States)

    Wollman, E E; Lei, C U; Weinstein, A J; Suh, J; Kronwald, A; Marquardt, F; Clerk, A A; Schwab, K C

    2015-08-28

    According to quantum mechanics, a harmonic oscillator can never be completely at rest. Even in the ground state, its position will always have fluctuations, called the zero-point motion. Although the zero-point fluctuations are unavoidable, they can be manipulated. Using microwave frequency radiation pressure, we have manipulated the thermal fluctuations of a micrometer-scale mechanical resonator to produce a stationary quadrature-squeezed state with a minimum variance of 0.80 times that of the ground state. We also performed phase-sensitive, back-action evading measurements of a thermal state squeezed to 1.09 times the zero-point level. Our results are relevant to the quantum engineering of states of matter at large length scales, the study of decoherence of large quantum systems, and for the realization of ultrasensitive sensing of force and motion. Copyright © 2015, American Association for the Advancement of Science.

  13. Contact geometry and quantum mechanics

    Science.gov (United States)

    Herczeg, Gabriel; Waldron, Andrew

    2018-06-01

    We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime". We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics.

  14. Quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM).

    Science.gov (United States)

    Sinitskiy, Anton V; Voth, Gregory A

    2018-01-07

    Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantum mechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantum mechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed.

  15. Quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM)

    Science.gov (United States)

    Sinitskiy, Anton V.; Voth, Gregory A.

    2018-01-01

    Numerous molecular systems, including solutions, proteins, and composite materials, can be modeled using mixed-resolution representations, of which the quantum mechanics/molecular mechanics (QM/MM) approach has become the most widely used. However, the QM/MM approach often faces a number of challenges, including the high cost of repetitive QM computations, the slow sampling even for the MM part in those cases where a system under investigation has a complex dynamics, and a difficulty in providing a simple, qualitative interpretation of numerical results in terms of the influence of the molecular environment upon the active QM region. In this paper, we address these issues by combining QM/MM modeling with the methodology of "bottom-up" coarse-graining (CG) to provide the theoretical basis for a systematic quantum-mechanical/coarse-grained molecular mechanics (QM/CG-MM) mixed resolution approach. A derivation of the method is presented based on a combination of statistical mechanics and quantum mechanics, leading to an equation for the effective Hamiltonian of the QM part, a central concept in the QM/CG-MM theory. A detailed analysis of different contributions to the effective Hamiltonian from electrostatic, induction, dispersion, and exchange interactions between the QM part and the surroundings is provided, serving as a foundation for a potential hierarchy of QM/CG-MM methods varying in their accuracy and computational cost. A relationship of the QM/CG-MM methodology to other mixed resolution approaches is also discussed.

  16. Theoretical physics. Quantum mechanics

    International Nuclear Information System (INIS)

    Rebhan, Eckhard

    2008-01-01

    From the first in two comprehensive volumes appeared Theoretical Physics of the author by this after Mechanics and Electrodynamics also Quantum mechanics appears as thinner single volume. First the illustrative approach via wave mechanics is reproduced. The more abstract Hilbert-space formulation introduces the author later by postulates, which are because of the preceding wave mechanics sufficiently plausible. All concepts of quantum mechanics, which contradict often to the intuitive understanding formed by macroscopic experiences, are extensively discussed and made by means of many examples as well as problems - in the largest part provided with solutions - understandable. To the interpretation of quantum mechanics an extensive special chapter is dedicated. this book arose from courses on theoretical physics, which the author has held at the Heinrich-Heine University in Duesseldorf, and was in numerous repetitions fitted to the requirement of the studyings. it is so designed that it is also after the study suited as reference book or for the renewing. All problems are very thoroughly and such extensively studied that each step is separately reproducible. About motivation and good understandability is cared much

  17. Quantum mechanics and computation

    International Nuclear Information System (INIS)

    Cirac Sasturain, J. I.

    2000-01-01

    We review how some of the basic principles of Quantum Mechanics can be used in the field of computation. In particular, we explain why a quantum computer can perform certain tasks in a much more efficient way than the computers we have available nowadays. We give the requirements for a quantum system to be able to implement a quantum computer and illustrate these requirements in some particular physical situations. (Author) 16 refs

  18. Lectures on quantum mechanics

    International Nuclear Information System (INIS)

    Weinberg, Steven

    2015-01-01

    Quantum mechanics represents the central revolution of modern natural science and reaches in its importance farely beyond physics. Neither chemistry nor biology on the molecular scale would be understandable without it. Modern information technology from the laptop over the mobile telephone and the flat screen until the supercomputer would be unthinkable without quantum-mechanical effects. It desribes the world on the atomic and subatomic scale and is by this the starting point of our modern worldview. The Nobel-prize carrier Steven Weinberg has done ever among others by his theory of the unification of the weak and the electromagnetic interaction one of the most important contributions to this revolution. In this book he reproduces his personal view of quantum mechanics, which captivates by its strictly logic construction, precise linguistic representation, and mathematical clearness and completeness. This book appeals to studyings of natural sciences, especially of physics. Accompanied is the test by exercise problems, which allow the studying to apply immediately the knowledge, but also test their understanding. Because of its precision and clearness ''Lectures on Quantum Mechanics'' by Weinberg is also essentially suited for the self-study.

  19. Equivalence principle and quantum mechanics: quantum simulation with entangled photons.

    Science.gov (United States)

    Longhi, S

    2018-01-15

    Einstein's equivalence principle (EP) states the complete physical equivalence of a gravitational field and corresponding inertial field in an accelerated reference frame. However, to what extent the EP remains valid in non-relativistic quantum mechanics is a controversial issue. To avoid violation of the EP, Bargmann's superselection rule forbids a coherent superposition of states with different masses. Here we suggest a quantum simulation of non-relativistic Schrödinger particle dynamics in non-inertial reference frames, which is based on the propagation of polarization-entangled photon pairs in curved and birefringent optical waveguides and Hong-Ou-Mandel quantum interference measurement. The photonic simulator can emulate superposition of mass states, which would lead to violation of the EP.

  20. The formalisms of quantum mechanics an introduction

    CERN Document Server

    David, Francois

    2015-01-01

    These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and ...

  1. Interactive Simulations to Support Quantum Mechanics Instruction for Chemistry Students

    Science.gov (United States)

    Kohnle, Antje; Benfield, Cory; Hahner, Georg; Paetkau, Mark

    2017-01-01

    The QuVis Quantum Mechanics Visualization Project provides freely available research-based interactive simulations with accompanying activities for the teaching and learning of quantum mechanics across a wide range of topics and levels. This article gives an overview of some of the simulations and describes their use in an introductory physical…

  2. Quantum mechanics

    CERN Document Server

    Rae, Alastair I M

    2007-01-01

    PREFACESINTRODUCTION The Photoelectric Effect The Compton Effect Line Spectra and Atomic Structure De Broglie Waves Wave-Particle Duality The Rest of This Book THE ONE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Time-Dependent Schrödinger Equation The Time-Independent Schrödinger Equation Boundary ConditionsThe Infinite Square Well The Finite Square Well Quantum Mechanical Tunneling The Harmonic Oscillator THE THREE-DIMENSIONAL SCHRÖDINGER EQUATIONS The Wave Equations Separation in Cartesian Coordinates Separation in Spherical Polar Coordinates The Hydrogenic Atom THE BASIC POSTULATES OF QUANTUM MEC

  3. Quantum mechanics & the big world

    NARCIS (Netherlands)

    Wezel, Jasper van

    2007-01-01

    Quantum Mechanics is one of the most successful physical theories of the last century. It explains physical phenomena from the smallest to the largest lengthscales. Despite this triumph, quantum mechanics is often perceived as a mysterious theory, involving superposition states that are alien to our

  4. Quantum-mechanical computers and uncomputability

    International Nuclear Information System (INIS)

    Lloyd, S.

    1993-01-01

    The time evolution operator for any quantum-mechanical computer is diagonalizable, but to obtain the diagonal decomposition of a program state of the computer is as hard as actually performing the computation corresponding to the program. In particular, if a quantum-mechanical system is capable of universal computation, then the diagonal decomposition of program states is uncomputable. As a result, in a universe in which local variables support universal computation, a quantum-mechanical theory for that universe that supplies its spectrum cannot supply the spectral decomposition of the computational variables. A ''theory of everything'' can be simultaneously correct and fundamentally incomplete

  5. Variational principle in quantum mechanics

    International Nuclear Information System (INIS)

    Popiez, L.

    1986-01-01

    The variational principle in a standard, path integral formulation of quantum mechanics (as proposed by Dirac and Feynman) appears only in the context of a classical limit n to 0 and manifests itself through the method of abstract stationary phase. Symbolically it means that a probability amplitude averaged over trajectories denotes a classical evolution operator for points in a configuration space. There exists, however, the formulation of quantum dynamics in which variational priniple is one of basic postulates. It is explained that the translation between stochastic and quantum mechanics in this case can be understood as in Nelson's stochastic mechanics

  6. A quantum information approach to statistical mechanics

    International Nuclear Information System (INIS)

    Cuevas, G.

    2011-01-01

    The field of quantum information and computation harnesses and exploits the properties of quantum mechanics to perform tasks more efficiently than their classical counterparts, or that may uniquely be possible in the quantum world. Its findings and techniques have been applied to a number of fields, such as the study of entanglement in strongly correlated systems, new simulation techniques for many-body physics or, generally, to quantum optics. This thesis aims at broadening the scope of quantum information theory by applying it to problems in statistical mechanics. We focus on classical spin models, which are toy models used in a variety of systems, ranging from magnetism, neural networks, to quantum gravity. We tackle these models using quantum information tools from three different angles. First, we show how the partition function of a class of widely different classical spin models (models in different dimensions, different types of many-body interactions, different symmetries, etc) can be mapped to the partition function of a single model. We prove this by first establishing a relation between partition functions and quantum states, and then transforming the corresponding quantum states to each other. Second, we give efficient quantum algorithms to estimate the partition function of various classical spin models, such as the Ising or the Potts model. The proof is based on a relation between partition functions and quantum circuits, which allows us to determine the quantum computational complexity of the partition function by studying the corresponding quantum circuit. Finally, we outline the possibility of applying quantum information concepts and tools to certain models of dis- crete quantum gravity. The latter provide a natural route to generalize our results, insofar as the central quantity has the form of a partition function, and as classical spin models are used as toy models of matter. (author)

  7. Supersymmetric quantum mechanics: another nontrivial quantum superpotential

    International Nuclear Information System (INIS)

    Cervero, J.M.

    1991-01-01

    A nontrivial example of a quantum superpotential in the framework of supersymmetric quantum mechanics is constructed using integrable soliton-like functions. The model is shown to be fully solvable and some consequences regarding the physical properties of the model such as transparence and boundary effects are discussed. (orig.)

  8. Quantum mechanical determination of atomic polarizabilities of ionic liquids.

    Science.gov (United States)

    Heid, Esther; Szabadi, András; Schröder, Christian

    2018-04-25

    The distribution of a molecule's polarizability to individual atomic sites is inevitable to develop accurate polarizable force fields. We present the direct quantum mechanical calculation of atomic polarizabilities of 27 common ionic liquids. The method is superior to previously published distribution routines based on large databases of the molecular polarizability, and enables the correct description of any ionic liquid and its peculiarities within the quantum mechanical framework.

  9. Quantum mechanics in a nutshell

    CERN Document Server

    Mahan, Gerald D

    2009-01-01

    Covering the fundamentals as well as many special topics of current interest, this is the most concise, up-to-date, and accessible graduate-level textbook on quantum mechanics available. Written by Gerald Mahan, a distinguished research physicist and author of an acclaimed textbook on many-particle physics, Quantum Mechanics in a Nutshell is the distillation of many years' teaching experience. Emphasizing the use of quantum mechanics to describe actual quantum systems such as atoms and solids, and rich with interesting applications, the book proceeds from solving for the properties of a single particle in potential; to solving for two particles (the helium atom); to addressing many-particle systems. Applications include electron gas, magnetism, and Bose-Einstein Condensation; examples are carefully chosen and worked; and each chapter has numerous homework problems, many of them original

  10. Recent trials to verify quantum mechanics

    International Nuclear Information System (INIS)

    Paty, M.

    1974-01-01

    An account of the experiments which deal with the verification of Quantum Mechanics and the hidden variable problem is made. First, the well-known EPR paradox is recalled which, in spite of its refutation by Bohr, was the starting point of the questionning on the completeness of Quantum Mechanics and of hidden variable theories; and then Bell's theorem, which shows that the two approaches, Quantum Mechanics and hidden variables, can be put in contradiction. Thereafter the various types of experiments which have been carried out on that subject, mostly concerning the correlation measurements between two photons emitted by a quantum system are described. The most recent experimental results are diverging, some of them to confirm and some others to contradict quantum mechanics. A review of these is given; and a discussion is presented about their possible implications [fr

  11. Theoretical physics vol. 2. Quantum mechanics, relativistic quantum mechanics, quantum field theory, elementar-particle theory, thermodynamics and statistics

    International Nuclear Information System (INIS)

    Rebhan, E.

    2005-01-01

    The present second volume treats quantum mechanics, relativistic quantum mechanics, the foundations of quantum-field and elementary-particle theory as well as thermodynamics and statistics. Both volumes comprehend all fields, which are usually offered in a course about theoretical physics. In all treated fields a very careful introduction to the basic natural laws forms the starting point, whereby it is thoroughly analysed, which of them is based on empirics, which is logically deducible, and which role play basic definitions. Extendingly the matter extend of the corresponding courses starting from the relativistic quantum theory an introduction to the elementary particles is developed. All problems are very thoroughly and such extensively studied, that each step is singularly reproducible. On motivation and good understandability is cared much about. The mixing of mathematical difficulties with problems of physical nature often obstructive in the learning is so circumvented, that important mathematical methods are presented in own chapters (for instance Hilbert spaces, Lie groups). By means of many examples and problems (for a large part with solutions) the matter worked out is deepened and exercised. Developments, which are indeed important, but seem for the first approach abandonable, are pursued in excurses. This book starts from courses, which the author has held at the Heinrich-Heine university in Duesseldorf, and was in many repetitions fitted to the requirements of the students. It is conceived in such a way, that it is also after the study suited as dictionary or for the regeneration

  12. Time in quantum mechanics

    CERN Document Server

    Mayato, R; Egusquiza, I

    2002-01-01

    The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the theory. This book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. This multiauthored book, written as an introductory guide for the non-initiated as well as a useful source of information for the expert, covers many of the open questions. A brief historical overview is to be found in the introduction. It is followed by 12 chapters devoted to conceptual and theoretical investigations as well as experimental issues in quantum-mechanical time measurements. This unique monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics.

  13. Stochastic incompleteness of quantum mechanics

    International Nuclear Information System (INIS)

    Suppes, P.; Zanotti, M.

    1976-01-01

    This article brings out in as conceptually clear terms as possible what seems to be a major incompleteness in the probability theory of particles offered by classical quantum mechanics. The exact nature of this incompleteness is illustrated by consideration of some simple quantum-mechanical examples. In addition, these examples are contrasted with the fundamental assumptions of Brownian motion in classical physics on the one hand, and with a controversey of a deecade ago in mathematical physchology. The central claim is that clasical quantum mechanics is radically incomplete in its probabilistic account of the motion of particles. In the last part of the article the time-dependent joint distribution of position and momentum of the linear harmonic oscillator is derived, and it is shown how the apparently physically paradoxical statistical independence of position and momentum has a natural explanation. The explanation is given within the framework of the non-quantum-mechanical stochastic theory constructed for such oscillators. (Auth.)

  14. Hilbert space and quantum mechanics

    CERN Document Server

    Gallone, Franco

    2015-01-01

    The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for individual study. The principles of quantum mechanics are discussed with complete mathematical accuracy and an effort is made to always trace them back to the experimental reality that lies at their root. The treatment of quantum mechanics is axiomatic, with definitions followed by propositions proved in a mathematical fashion. No previous knowledge of quantum mechanics is required. This book is designed so that parts of it can be easily used for various courses in mathematics and mathematical physics, as suggested in the Pref...

  15. Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

    International Nuclear Information System (INIS)

    Yang, C.-D.

    2006-01-01

    This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schroedinger equation. Using complex canonical variables, a formal proof of the quantization axiom p → p = -ih∇, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov-Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion

  16. From quantum mechanics to universal structures of conceptualization and feedback on quantum mechanics

    International Nuclear Information System (INIS)

    Mugur-Schaechter, M.

    1993-01-01

    In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (states of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a general syntax of relativized conceptualization where any description is explicity and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualiztion. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides towards the answers. Globally the results obtained provide a basis for the future attempts at a general mathematical representation of the processes of conceptualization

  17. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals.

    Science.gov (United States)

    Sinitskiy, Anton V; Voth, Gregory A

    2015-09-07

    Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

  18. A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

    International Nuclear Information System (INIS)

    Sinitskiy, Anton V.; Voth, Gregory A.

    2015-01-01

    Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman’s imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments

  19. Moessbauer neutrinos in quantum mechanics and quantum field theory

    International Nuclear Information System (INIS)

    Kopp, Joachim

    2009-01-01

    We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Moessbauer neutrino oscillations. First, we compute the combined rate Γ of Moessbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for Γ is identical to the one obtained previously [1] for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Moessbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Moessbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.

  20. Quantum Mechanics as Classical Physics

    OpenAIRE

    Sebens, CT

    2015-01-01

    Here I explore a novel no-collapse interpretation of quantum mechanics which combines aspects of two familiar and well-developed alternatives, Bohmian mechanics and the many-worlds interpretation. Despite reproducing the empirical predictions of quantum mechanics, the theory looks surprisingly classical. All there is at the fundamental level are particles interacting via Newtonian forces. There is no wave function. However, there are many worlds.

  1. On quantum mechanical phase-space wave functions

    DEFF Research Database (Denmark)

    Wlodarz, Joachim J.

    1994-01-01

    An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...... function. The relationship to the recent results by Torres-Vega and Frederick [J. Chem. Phys. 98, 3103 (1993)] is also discussed....

  2. Foundations of Quantum Mechanics and Quantum Computation

    Science.gov (United States)

    Aspect, Alain; Leggett, Anthony; Preskill, John; Durt, Thomas; Pironio, Stefano

    2013-03-01

    I ask the question: What can we infer about the nature and structure of the physical world (a) from experiments already done to test the predictions of quantum mechanics (b) from the assumption that all future experiments will agree with those predictions? I discuss existing and projected experiments related to the two classic paradoxes of quantum mechanics, named respectively for EPR and Schrödinger's Cat, and show in particular that one natural conclusion from both types of experiment implies the abandonment of the concept of macroscopic counterfactual definiteness.

  3. Solvable potentials derived from supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Levai, G.

    1994-01-01

    The introduction of supersymmetric quantum mechanics has generated renewed interest in solvable problems of non-relativistic quantum mechanics. This approach offers an elegant way to describe different, but isospectral potentials by interpreting the degeneracy of their energy levels in terms of supersymmetry. The original ideas of supersymmetric quantum mechanics have been developed further in many respects in the past ten years, and have been applied to a large variety of physical problems. The purpose of this contribution is to give a survey of supersymmetric quantum mechanics and its applications to solvable quantum mechanical potentials. Its relation to other models describing isospectral potentials is also discussed here briefly, as well as some of its practical applications in various branches of physics. (orig.)

  4. Stochastic quantum mechanics and quantum spacetime

    International Nuclear Information System (INIS)

    Prugovecki, E.

    1984-01-01

    This monograph deals in part with the physical, mathematical and epistemological reasons behind the failure of past theoretical frameworks, including conventional relativistic quantum mechanics, to bring about a conssistent unification of relativity with quantum theory. The assessment of the past record is set in an historical perspective by citing from original sources, some of which might be partly forgotten or are not that well known, but forcefully illustrate the motivations and goals of the foudners of relativity and quantum theory as they set about developing their respetive disciplines. The proposed framework for unification, which constitutes the bulk of this book, embraces classical as well as quantum theories by implementing an epsitemic idea first put forth by M. Born, namely that all deterministic values for measurable quantitites. The framework gives rise to a whole range of yet unresearched problems, whose solutions are bound to shed some light on the relationship between relativity and quantum theories of the most fundamental physical and mathematical leves. (author). refs.; figs.; tabs

  5. Unwaving quantum mechanics

    International Nuclear Information System (INIS)

    Torre, A.C. de la; Mirabella, D.; Izus, G.

    1990-01-01

    The so called diffraction experiments are explained making no reference to any wave whatsoever. It is proposed that these waves are a mere mathematical artifact without any physical reality. If propensities and transmission between them are accepted as a physical reality, then the wave concept can be set aside along with duality and complementarity, thus eliminating controversy on the interpretation of quantum mechanics. An outline is made of the formulation of the theory based on the preparation of the system according to propensities and the transmission between them. (Author). 19 refs., 1 fig

  6. Theoretical physics IV. Quantum mechanics with problems in MAPLE

    International Nuclear Information System (INIS)

    Reinecker, Peter; Schulz, Michael; Schulz, Beatrix M.

    2008-01-01

    Quantum mechanics 2 is the fourth volume of the new and unique series for theoretical physics with Maple applications. This from basics newly concipated series mediates theoretical physics from contemporary view and in a way referring to a comprehensive lecture experience. Extensively and completely in five consecutively appearing volumes classical mechanics, electrodynamics, quantum mechanics 1 and 2, as well as statistical physics and thermodynamics are presented. Additionally for the elegant and extensive presentation on an each added CP applications for MAPLE trademark are contained, the software, which at more and more university is already applied in the lecture. They allow the experimenting with theory - and facilitate the understanding essentially. The present volume mediates extending, more complex contents of quantum mechanics, which are based on volume III of the series

  7. Time Asymmetric Quantum Mechanics

    Directory of Open Access Journals (Sweden)

    Arno R. Bohm

    2011-09-01

    Full Text Available The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1 for states or the Heisenberg equation (6a for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus and observables (defined by a registration apparatus (detector. If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t_0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

  8. Science Academies' Refresher Course in Quantum Mechanics

    Indian Academy of Sciences (India)

    IAS Admin

    2013-02-28

    Feb 28, 2013 ... A Refresher Course in Quantum Mechanics for college/university teachers ... The Course will cover the basic and advanced topics of Quantum ... Module 1:- Principles of Quantum Mechanics (with associated mathematics), ...

  9. Relativistic quantum mechanics; Mecanique quantique relativiste

    Energy Technology Data Exchange (ETDEWEB)

    Ollitrault, J.Y. [CEA Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique]|[Universite Pierre et Marie Curie, 75 - Paris (France)

    1998-12-01

    These notes form an introduction to relativistic quantum mechanics. The mathematical formalism has been reduced to the minimum in order to enable the reader to calculate elementary physical processes. The second quantification and the field theory are the logical followings of this course. The reader is expected to know analytical mechanics (Lagrangian and Hamiltonian), non-relativistic quantum mechanics and some basis of restricted relativity. The purpose of the first 3 chapters is to define the quantum mechanics framework for already known notions about rotation transformations, wave propagation and restricted theory of relativity. The next 3 chapters are devoted to the application of relativistic quantum mechanics to a particle with 0,1/5 and 1 spin value. The last chapter deals with the processes involving several particles, these processes require field theory framework to be thoroughly described. (A.C.) 2 refs.

  10. Noncommutative quantum mechanics

    Science.gov (United States)

    Gamboa, J.; Loewe, M.; Rojas, J. C.

    2001-09-01

    A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.

  11. Facets of contextual realism in quantum mechanics

    International Nuclear Information System (INIS)

    Pan, Alok Kumar; Home, Dipankar

    2011-01-01

    In recent times, there is an upsurge of interest in demonstrating the quantum contextuality. In this proceedings, we explore the two different forms of arguments that have been used for showing the contextual character of quantum mechanics. First line of study concerns the violations of the noncontextual realist models by quantum mechanics, where second line of study that is qualitatively distinct from the earlier one, demonstrates the contextuality within the formalism of quantum mechanics.

  12. QUANTUM MECHANICS WITHOUT STATISTICAL POSTULATES

    International Nuclear Information System (INIS)

    Geiger, G.

    2000-01-01

    The Bohmian formulation of quantum mechanics describes the measurement process in an intuitive way without a reduction postulate. Due to the chaotic motion of the hidden classical particle all statistical features of quantum mechanics during a sequence of repeated measurements can be derived in the framework of a deterministic single system theory

  13. Quantum mechanics and stochastic mechanics for compatible observables at different times

    International Nuclear Information System (INIS)

    Correggi, M.; Morchio, G.

    2002-01-01

    Bohm mechanics and Nelson stochastic mechanics are confronted with quantum mechanics in the presence of noninteracting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary states agree with quantum mechanics only in the case of product wave functions. By appropriate Bell-like inequalities it is shown that no classical theory, in particular no stochastic process, can reproduce the quantum mechanical correlations of position variables of noninteracting systems at different times

  14. The physics of quantum mechanics

    CERN Document Server

    Binney, James

    2014-01-01

    The Physics of Quantum Mechanics aims to give students a good understanding of how quantum mechanics describes the material world. It shows that the theory follows naturally from the use of probability amplitudes to derive probabilities. It stresses that stationary states are unphysical mathematical abstractions that enable us to solve the theory's governing equation, the time-dependent Schroedinger equation. Every opportunity is taken to illustrate the emergence of the familiarclassical, dynamical world through the quantum interference of stationary states. The text stresses the continuity be

  15. Stochastic mechanics and quantum theory

    International Nuclear Information System (INIS)

    Goldstein, S.

    1987-01-01

    Stochastic mechanics may be regarded as both generalizing classical mechanics to processes with intrinsic randomness, as well as providing the sort of detailed description of microscopic events declared impossible under the traditional interpretation of quantum mechanics. It avoids the many conceptual difficulties which arise from the assumption that quantum mechanics, i.e., the wave function, provides a complete description of (microscopic) physical reality. Stochastic mechanics presents a unified treatment of the microscopic and macroscopic domains, in which the process of measurement plays no special physical role and which reduces to Newtonian mechanics in the macroscopic limit

  16. Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

    International Nuclear Information System (INIS)

    Mostafazadeh, Ali

    2004-01-01

    With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂ t 2 +D)ψ(t)=0, where t is an element of R and D is a positive-definite operator acting in a Hilbert space H-tilde. In particular, we determine all the positive-definite inner products on the space H of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of H uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in H. Among these is a particular choice that generates t-translations in H and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in H, and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in L 2 R+L 2 R, show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the

  17. Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

    Science.gov (United States)

    Mostafazadeh, Ali

    2004-01-01

    With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂t2+D)ψ(t)=0, where t∈R and D is a positive-definite operator acting in a Hilbert space H~. In particular, we determine all the positive-definite inner products on the space H of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of H uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in H. Among these is a particular choice that generates t-translations in H and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in H, and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in L2(R)⊕L2(R), show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is

  18. Quantum mechanics a modern development

    CERN Document Server

    Ballentine, Leslie E

    2015-01-01

    Although there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory. In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions ...

  19. Quantum mechanics in matrix form

    CERN Document Server

    Ludyk, Günter

    2018-01-01

    This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix  method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.

  20. Spacetime coarse grainings in nonrelativistic quantum mechanics

    International Nuclear Information System (INIS)

    Hartle, J.B.

    1991-01-01

    Sum-over-histories generalizations of nonrelativistic quantum mechanics are explored in which probabilities are predicted, not just for alternatives defined on spacelike surfaces, but for alternatives defined by the behavior of spacetime histories with respect to spacetime regions. Closed, nonrelativistic systems are discussed whose histories are paths in a given configuration space. The action and the initial quantum state are assumed fixed and given. A formulation of quantum mechanics is used which assigns probabilities to members of sets of alternative coarse-grained histories of the system, that is, to the individual classes of a partition of its paths into exhaustive and exclusive classes. Probabilities are assigned to those sets which decohere, that is, whose probabilities are consistent with the sum rules of probability theory. Coarse graining by the behavior of paths with respect to regions of spacetime is described. For example, given a single region, the set of all paths may be partitioned into those which never pass through the region and those which pass through the region at least once. A sum-over-histories decoherence functional is defined for sets of alternative histories coarse-grained by spacetime regions. Techniques for the definition and effective computation of the relevant sums over histories by operator-product formulas are described and illustrated by examples. Methods based on Euclidean stochastic processes are also discussed and illustrated. Models of decoherence and measurement for spacetime coarse grainings are described. Issues of causality are investigated. Such spacetime generalizations of nonrelativistic quantum mechanics may be useful models for a generalized quantum mechanics of spacetime geometry

  1. Noncommutative unification of general relativity and quantum mechanics

    International Nuclear Information System (INIS)

    Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw

    2005-01-01

    We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid Γ given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics

  2. Position-based quantum cryptography and catalytic computation

    NARCIS (Netherlands)

    Speelman, F.

    2016-01-01

    In this thesis, we present several results along two different lines of research. The first part concerns the study of position-based quantum cryptography, a topic in quantum cryptography. By combining quantum mechanics with special relativity theory, new cryptographic tasks can be developed that

  3. Emergence of classical theories from quantum mechanics

    International Nuclear Information System (INIS)

    Hájícek, P

    2012-01-01

    Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's 'first kind of dynamics', and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

  4. Emergence of quantum mechanics from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, C

    2009-01-01

    The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical interpretations to practical issues as quantum computing. In this note we demonstrate how quantum mechanics can emerge from classical statistical systems. We discuss conditions and circumstances for this to happen. Quantum systems describe isolated subsystems of classical statistical systems with infinitely many states. While infinitely many classical observables 'measure' properties of the subsystem and its environment, the state of the subsystem can be characterized by the expectation values of only a few probabilistic observables. They define a density matrix, and all the usual laws of quantum mechanics follow. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem.

  5. Quantum mechanics selected topics

    CERN Document Server

    Perelomov, Askold Mikhailovich

    1998-01-01

    It can serve as a good supplement to any quantum mechanics textbook, filling the gap between standard textbooks and higher-level books on the one hand and journal articles on the other. This book provides a detailed treatment of the scattering theory, multidimensional quasi-classical approximation, non-stationary problems for oscillators and the theory of unstable particles. It will be useful for postgraduate students and researchers who wish to find new, interesting information hidden in the depths of non-relativistic quantum mechanics.

  6. Quantum mechanics and its limits

    International Nuclear Information System (INIS)

    Lamehi-Rachti, M.; Mittig, W.

    1977-01-01

    Bell has shown (Bell's inequality) that local hidden variable theories lead to predictions in contradiction with quantum mechanics. This has been tested in low energy proton-proton scattering by the simultaneous measurement of the polarisation of the two protons. The results are in agreement with quantum mechanics and thus in contradiction with the inequality of Bell [fr

  7. A relational solution to the problem of time in quantum mechanics and quantum gravity: a fundamental mechanism for quantum decoherence

    International Nuclear Information System (INIS)

    Gambini, Rodolfo; Porto, Rafael A; Pullin, Jorge

    2004-01-01

    The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a 'clock'. Conditional probabilities are computed for variables of the system to take certain values when the 'clock' specifies a certain time. This framework is attractive in contexts where the assumption of usual quantum mechanics of the existence of an external, perfectly classical clock, appears unnatural, as in quantum cosmology. Until recently, there were problems with such constructions in ordinary quantum mechanics with additional difficulties in the context of constrained theories like general relativity. A scheme we recently introduced to consistently discretize general relativity removed such obstacles. Since the clock is now an object subject to quantum fluctuations, the resulting evolution in time is not exactly unitary and pure states decohere into mixed states. Here we work out in detail the type of decoherence generated, and we find it to be of Lindblad type. This is attractive since it implies that one can have loss of coherence without violating the conservation of energy. We apply the framework to a simple cosmological model to illustrate how a quantitative estimate of the effect could be computed. For most quantum systems it appears to be too small to be observed, although certain macroscopic quantum systems could in the future provide a testing ground for experimental observation

  8. How to solve path integrals in quantum mechanics

    International Nuclear Information System (INIS)

    Grosche, C.

    1994-10-01

    A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last 15 years, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given which will serve as a quick reference for solving path integrals. Explicit formulae for the so-called basic path integrals are presented on which our general scheme to classify and calculate path integrals in quantum mechanics is based. (orig.)

  9. Statistical algebraic approach to quantum mechanics

    International Nuclear Information System (INIS)

    Slavnov, D.A.

    2001-01-01

    The scheme for plotting the quantum theory with application of the statistical algebraic approach is proposed. The noncommutative algebra elements (observed ones) and nonlinear functionals on this algebra (physical state) are used as the primary constituents. The latter ones are associated with the single-unit measurement results. Certain physical state groups are proposed to consider as quantum states of the standard quantum mechanics. It is shown that the mathematical apparatus of the standard quantum mechanics may be reproduced in such a scheme in full volume [ru

  10. From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

    Science.gov (United States)

    Bergeron, H.

    2001-09-01

    Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence

  11. Information-theoretical approach to control of quantum-mechanical systems

    International Nuclear Information System (INIS)

    Kawabata, Shiro

    2003-01-01

    Fundamental limits on the controllability of quantum mechanical systems are discussed in the light of quantum information theory. It is shown that the amount of entropy-reduction that can be extracted from a quantum system by feedback controller is upper bounded by a sum of the decrease of entropy achievable in open-loop control and the mutual information between the quantum system and the controller. This upper bound sets a fundamental limit on the performance of any quantum controllers whose designs are based on the possibilities to attain low entropy states. An application of this approach pertaining to quantum error correction is also discussed

  12. Primer of quantum mechanics

    CERN Document Server

    Chester, Marvin

    2003-01-01

    Introductory text examines the classical quantum bead on a track: its state and representations; operator eigenvalues; harmonic oscillator and bound bead in a symmetric force field; and bead in a spherical shell. Also, spin, matrices and structure of quantum mechanics; simplest atom; indistinguishable particles; and stationary-state perturbation theory.

  13. Plasmonic resonances of nanoparticles from large-scale quantum mechanical simulations

    Science.gov (United States)

    Zhang, Xu; Xiang, Hongping; Zhang, Mingliang; Lu, Gang

    2017-09-01

    Plasmonic resonance of metallic nanoparticles results from coherent motion of its conduction electrons, driven by incident light. For the nanoparticles less than 10 nm in diameter, localized surface plasmonic resonances become sensitive to the quantum nature of the conduction electrons. Unfortunately, quantum mechanical simulations based on time-dependent Kohn-Sham density functional theory are computationally too expensive to tackle metal particles larger than 2 nm. Herein, we introduce the recently developed time-dependent orbital-free density functional theory (TD-OFDFT) approach which enables large-scale quantum mechanical simulations of plasmonic responses of metallic nanostructures. Using TD-OFDFT, we have performed quantum mechanical simulations to understand size-dependent plasmonic response of Na nanoparticles and plasmonic responses in Na nanoparticle dimers and trimers. An outlook of future development of the TD-OFDFT method is also presented.

  14. Classical- and quantum mechanical Coulomb scattering

    International Nuclear Information System (INIS)

    Gratzl, W.

    1987-01-01

    Because in textbooks the quantum mechanical Coulomb scattering is either ignored or treated unsatisfactory, the present work attempts to present a physically plausible, mathematically correct but elementary treatment in a way that it can be used in textbooks and lectures on quantum mechanics. Coulomb scattering is derived as a limiting case of a screened Coulomb potential (finite range) within a time dependent quantum scattering theory. The difference in the asymptotic conditions for potentials of finite versus infinite range leads back to the classical Coulomb scattering. In the classical framework many concepts of the quantum theory can be introduced and are useful in an intuitive understanding of the quantum theory. The differences between classical and quantum scattering theory are likewise useful for didactic purposes. (qui)

  15. Undergraduate quantum mechanics: lost opportunities for engaging motivated students?

    Science.gov (United States)

    Johansson, Anders

    2018-03-01

    Quantum mechanics is widely recognised as an important and difficult subject, and many studies have been published focusing on students’ conceptual difficulties. However, the sociocultural aspects of studying such an emblematic subject have not been researched to any large extent. This study explores students’ experiences of undergraduate quantum mechanics using qualitative analysis of semi-structured interview data. The results inform discussions about the teaching of quantum mechanics by adding a sociocultural dimension. Students pictured quantum mechanics as an intriguing subject that inspired them to study physics. The study environment they encountered when taking their first quantum mechanics course was however not always as inspiring as expected. Quantum mechanics instruction has commonly focused on the mathematical framework of quantum mechanics, and this kind of teaching was also what the interviewees had experienced. Two ways of handling the encounter with a traditional quantum mechanics course were identified in the interviews; either students accept the practice of studying quantum mechanics in a mathematical, exercise-centred way or they distance themselves from these practices and the subject. The students who responded by distancing themselves experienced a crisis and disappointment, where their experiences did not match the way they imagined themselves engaging with quantum mechanics. The implications of these findings are discussed in relation to efforts to reform the teaching of undergraduate quantum mechanics.

  16. Quantum Mechanics predicts evolutionary biology.

    Science.gov (United States)

    Torday, J S

    2018-07-01

    Nowhere are the shortcomings of conventional descriptive biology more evident than in the literature on Quantum Biology. In the on-going effort to apply Quantum Mechanics to evolutionary biology, merging Quantum Mechanics with the fundamentals of evolution as the First Principles of Physiology-namely negentropy, chemiosmosis and homeostasis-offers an authentic opportunity to understand how and why physics constitutes the basic principles of biology. Negentropy and chemiosmosis confer determinism on the unicell, whereas homeostasis constitutes Free Will because it offers a probabilistic range of physiologic set points. Similarly, on this basis several principles of Quantum Mechanics also apply directly to biology. The Pauli Exclusion Principle is both deterministic and probabilistic, whereas non-localization and the Heisenberg Uncertainty Principle are both probabilistic, providing the long-sought after ontologic and causal continuum from physics to biology and evolution as the holistic integration recognized as consciousness for the first time. Copyright © 2018 Elsevier Ltd. All rights reserved.

  17. Polarizable Force Field for DNA Based on the Classical Drude Oscillator: I. Refinement Using Quantum Mechanical Base Stacking and Conformational Energetics.

    Science.gov (United States)

    Lemkul, Justin A; MacKerell, Alexander D

    2017-05-09

    Empirical force fields seek to relate the configuration of a set of atoms to its energy, thus yielding the forces governing its dynamics, using classical physics rather than more expensive quantum mechanical calculations that are computationally intractable for large systems. Most force fields used to simulate biomolecular systems use fixed atomic partial charges, neglecting the influence of electronic polarization, instead making use of a mean-field approximation that may not be transferable across environments. Recent hardware and software developments make polarizable simulations feasible, and to this end, polarizable force fields represent the next generation of molecular dynamics simulation technology. In this work, we describe the refinement of a polarizable force field for DNA based on the classical Drude oscillator model by targeting quantum mechanical interaction energies and conformational energy profiles of model compounds necessary to build a complete DNA force field. The parametrization strategy employed in the present work seeks to correct weak base stacking in A- and B-DNA and the unwinding of Z-DNA observed in the previous version of the force field, called Drude-2013. Refinement of base nonbonded terms and reparametrization of dihedral terms in the glycosidic linkage, deoxyribofuranose rings, and important backbone torsions resulted in improved agreement with quantum mechanical potential energy surfaces. Notably, we expand on previous efforts by explicitly including Z-DNA conformational energetics in the refinement.

  18. Toy Models of a Nonassociative Quantum Mechanics

    International Nuclear Information System (INIS)

    Dzhunushaliev, V.

    2007-01-01

    Toy models of a nonassociative quantum mechanics are presented. The Heisenberg equation of motion is modified using a nonassociative commutator. Possible physical applications of a nonassociative quantum mechanics are considered. The idea is discussed that a nonassociative algebra could be the operator language for the nonperturbative quantum theory. In such approach the nonperturbative quantum theory has observables and un observables quantities.

  19. Chaos. Possible underpinnings for quantum mechanics?

    International Nuclear Information System (INIS)

    McHarris, Wm.C.

    2004-01-01

    Alternative, parallel explanations for a number of counter-intuitive concepts connected with the foundations of quantum mechanics can be constructed in terms of nonlinear dynamics. These include ideas as diverse as the statistical exponential decay law and spontaneous symmetry breaking to decoherence itself and the inference from violations of Bell's inequality that local reality is ruled out in hidden variable extensions of quantum mechanics. Such alternative explanations must not be taken as demonstrations of nonlinear underpinnings for quantum mechanics, but they do raise the possibility of their existence. In this article I delve a bit into ideas connected with the exponential decay law and with Bell's inequality as demonstrations. Then an investigation of the Klein-Gordon equation shows that it should not come as a complete surprise that quantum mechanics just might contain fundamental nonlinearities. (author)

  20. Effective equations for the quantum pendulum from momentous quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Hernandez, Hector H.; Chacon-Acosta, Guillermo [Universidad Autonoma de Chihuahua, Facultad de Ingenieria, Nuevo Campus Universitario, Chihuahua 31125 (Mexico); Departamento de Matematicas Aplicadas y Sistemas, Universidad Autonoma Metropolitana-Cuajimalpa, Artificios 40, Mexico D. F. 01120 (Mexico)

    2012-08-24

    In this work we study the quantum pendulum within the framework of momentous quantum mechanics. This description replaces the Schroedinger equation for the quantum evolution of the system with an infinite set of classical equations for expectation values of configuration variables, and quantum dispersions. We solve numerically the effective equations up to the second order, and describe its evolution.

  1. Elucidating reaction mechanisms on quantum computers

    Science.gov (United States)

    Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

    2017-01-01

    With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources. PMID:28674011

  2. Elucidating reaction mechanisms on quantum computers

    Science.gov (United States)

    Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

    2017-07-01

    With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

  3. Elucidating reaction mechanisms on quantum computers.

    Science.gov (United States)

    Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias

    2017-07-18

    With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

  4. Quantum mechanics as total physical theory

    International Nuclear Information System (INIS)

    Slavnov, D.A.

    2002-01-01

    It is shown that the principles of the total physical theory and conclusions of the standard quantum mechanics are not at such an antagonistic variance as it is usually accepted. The axioms, which make it possible to plot the renewed mathematical scheme of the quantum mechanics are formulated within the frames of the algebraic approach. The above scheme includes the standard mathematical apparatus of the quantum mechanics. Simultaneously there exists the mathematical object, which adequately describes the individual experiment. The examples of applying the proposed scheme is presented [ru

  5. Introduction to quantum statistical mechanics

    International Nuclear Information System (INIS)

    Bogolyubov, N.N.; Bogolyubov, N.N.

    1980-01-01

    In a set of lectures, which has been delivered at the Physical Department of Moscow State University as a special course for students represented are some basic ideas of quantum statistical mechanics. Considered are in particular, the Liouville equations in classical and quantum mechanics, canonical distribution and thermodynamical functions, two-time correlation functions and Green's functions in the theory of thermal equilibrium

  6. Quantum mechanics in coherent algebras on phase space

    International Nuclear Information System (INIS)

    Lesche, B.; Seligman, T.H.

    1986-01-01

    Quantum mechanics is formulated on a quantum mechanical phase space. The algebra of observables and states is represented by an algebra of functions on phase space that fulfills a certain coherence condition, expressing the quantum mechanical superposition principle. The trace operation is an integration over phase space. In the case where the canonical variables independently run from -infinity to +infinity the formalism reduces to the representation of quantum mechanics by Wigner distributions. However, the notion of coherent algebras allows to apply the formalism to spaces for which the Wigner mapping is not known. Quantum mechanics of a particle in a plane in polar coordinates is discussed as an example. (author)

  7. Quantum mechanics. Introduction. 6. rev. and enl. ed.

    International Nuclear Information System (INIS)

    Greiner, W.

    2005-01-01

    The following topics are dealt with: Quantization of physical quantities, radiation laws, the wave aspect of matter, mathematical foundations of quantum mechanics, ther Schroedinger equation, the harmonic oscillator, the transition from classical to quantum mechanics, a charged particle in the electromagnetic field, the hydrogen atom, perturbation theory and approximation procedures, spin, a nonrelativistic wave equation with spin, systems of identical particles, the formal scheme of quantum mechanics, conceptions and philosophical problems of quantum mechanics. (HSI)

  8. Macroscopic quantum mechanics: theory and experimental concepts of optomechanics

    International Nuclear Information System (INIS)

    Chen Yanbei

    2013-01-01

    Rapid experimental progress has recently allowed the use of light to prepare macroscopic mechanical objects into nearly pure quantum states. This research field of quantum optomechanics opens new doors towards testing quantum mechanics, and possibly other laws of physics, in new regimes. In the first part of this article, I will review a set of techniques of quantum measurement theory that are often used to analyse quantum optomechanical systems. Some of these techniques were originally designed to analyse how a classical driving force passes through a quantum system, and can eventually be detected with an optimal signal-to-noise ratio—while others focus more on the quantum-state evolution of a mechanical object under continuous monitoring. In the second part of this article, I will review a set of experimental concepts that will demonstrate quantum mechanical behaviour of macroscopic objects—quantum entanglement, quantum teleportation and the quantum Zeno effect. Taking the interplay between gravity and quantum mechanics as an example, I will review a set of speculations on how quantum mechanics can be modified for macroscopic objects, and how these speculations—and their generalizations—might be tested by optomechanics. (invited review)

  9. Supersymmetric quantum mechanics on n-dimensional manifolds

    International Nuclear Information System (INIS)

    O'Connor, M.

    1990-01-01

    In this thesis the author investigates the properties of the supersymmetric path integral on Riemannian manifolds. Chapter 1 is a brief introduction to supersymmetric path integral can be defined as the continuum limit of a discrete supersymmetric path integral. In Chapter 3 he shows that point canonical transformations in the path integral for ordinary quantum mechanics can be performed naively provided one uses the supersymmetric path integral. Chapter 4 generalizes the results of chapter 3 to include the propagation of all the fermion sectors in supersymmetric quantum mechanics. In Chapter 5 he shows how the properties of supersymmetric quantum mechanics can be used to investigate topological quantum mechanics

  10. The mechanism of suppression of quantum transitions (quantum whirligig)

    International Nuclear Information System (INIS)

    Buts, V.A.

    2010-01-01

    The mechanism allowing to stabilize of a state of quantum systems is considered. And, the initial condition can correspond both for excited state and for not excited, stationary state. The considered mechanism for the first time was offered for the excited states, and has received the name as quantum whirligig (QWE). In this work the close connection of the considered mechanism with Zeno effect is shown. The considerations are stated, that many experimental results, which are interpreted as observation of Zeno effect, apparently, correspond to QWE.

  11. Quo Vadis Quantum Mechanics?

    CERN Document Server

    Dolev, S; Kolenda, N

    2005-01-01

    For more than a century, quantum mechanics has served as a very powerful theory that has expanded physics and technology far beyond their classical limits, yet it has also produced some of the most difficult paradoxes known to the human mind. This book represents the combined efforts of sixteen of today's most eminent theoretical physicists to lay out future directions for quantum physics. The authors include Yakir Aharonov, Anton Zeilinger; the Nobel laureates Anthony Leggett and Geradus 't Hooft; Basil Hiley, Lee Smolin and Henry Stapp. Following a foreword by Roger Penrose, the individual chapters address questions such as quantum non-locality, the measurement problem, quantum insights into relativity, cosmology and thermodynamics, and the possible bearing of quantum phenomena on biology and consciousness.

  12. Physics-based scoring of protein-ligand interactions: explicit polarizability, quantum mechanics and free energies.

    Science.gov (United States)

    Bryce, Richard A

    2011-04-01

    The ability to accurately predict the interaction of a ligand with its receptor is a key limitation in computer-aided drug design approaches such as virtual screening and de novo design. In this article, we examine current strategies for a physics-based approach to scoring of protein-ligand affinity, as well as outlining recent developments in force fields and quantum chemical techniques. We also consider advances in the development and application of simulation-based free energy methods to study protein-ligand interactions. Fuelled by recent advances in computational algorithms and hardware, there is the opportunity for increased integration of physics-based scoring approaches at earlier stages in computationally guided drug discovery. Specifically, we envisage increased use of implicit solvent models and simulation-based scoring methods as tools for computing the affinities of large virtual ligand libraries. Approaches based on end point simulations and reference potentials allow the application of more advanced potential energy functions to prediction of protein-ligand binding affinities. Comprehensive evaluation of polarizable force fields and quantum mechanical (QM)/molecular mechanical and QM methods in scoring of protein-ligand interactions is required, particularly in their ability to address challenging targets such as metalloproteins and other proteins that make highly polar interactions. Finally, we anticipate increasingly quantitative free energy perturbation and thermodynamic integration methods that are practical for optimization of hits obtained from screened ligand libraries.

  13. EDITORIAL: Focus on Mechanical Systems at the Quantum Limit FOCUS ON MECHANICAL SYSTEMS AT THE QUANTUM LIMIT

    Science.gov (United States)

    Aspelmeyer, Markus; Schwab, Keith

    2008-09-01

    The last five years have witnessed an amazing development in the field of nano- and micromechanics. What was widely considered fantasy ten years ago is about to become an experimental reality: the quantum regime of mechanical systems is within reach of current experiments. Two factors (among many) have contributed significantly to this situation. As part of the widespread effort into nanoscience and nanofabrication, it is now possible to produce high-quality nanomechanical and micromechanical resonators, spanning length scales of millimetres to nanometres, and frequencies from kilohertz to gigahertz. Researchers coupled these mechanical elements to high-sensitivity actuation and readout systems such as single-electron transistors, quantum dots, atomic point contacts, SQUID loops, high-finesse optical or microwave-cavities etc. Some of these ultra-sensitive readout schemes are in principle capable of detection at the quantum limit and a large part of the experimental effort is at present devoted to achieving this. On the other hand, the fact that the groups working in the field come from various different physics backgrounds—the authors of this editorial are a representative sample—has been a constant source of inspiration for helpful theoretical and experimental tools that have been adapted from other fields to the mechanical realm. To name just one example: ideas from quantum optics have led to the recent demonstration (both in theory and experiment) that coupling a mechanical resonator to a high-finesse optical cavity can be fully analogous to the well-known sideband-resolved laser cooling of ions and hence is capable in principle of cooling a mechanical mode into its quantum ground state. There is no doubt that such interdisciplinarity has been a crucial element for the development of the field. It is interesting to note that a very similar sociological phenomenon occurred earlier in the quantum information community, an area which is deeply enriched by the

  14. Foundations of a spacetime path formalism for relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Seidewitz, Ed

    2006-01-01

    Quantum field theory is the traditional solution to the problems inherent in melding quantum mechanics with special relativity. However, it has also long been known that an alternative first-quantized formulation can be given for relativistic quantum mechanics, based on the parametrized paths of particles in spacetime. Because time is treated similarly to the three space coordinates, rather than as an evolution parameter, such a spacetime approach has proved particularly useful in the study of quantum gravity and cosmology. This paper shows how a spacetime path formalism can be considered to arise naturally from the fundamental principles of the Born probability rule, superposition, and Poincare invariance. The resulting formalism can be seen as a foundation for a number of previous parametrized approaches in the literature, relating, in particular, 'off-shell' theories to traditional on-shell quantum field theory. It reproduces the results of perturbative quantum field theory for free and interacting particles, but provides intriguing possibilities for a natural program for regularization and renormalization. Further, an important consequence of the formalism is that a clear probabilistic interpretation can be maintained throughout, with a natural reduction to nonrelativistic quantum mechanics

  15. A new approach to shortest paths on networks based on the quantum bosonic mechanism

    Energy Technology Data Exchange (ETDEWEB)

    Jiang Xin; Wang Hailong; Tang Shaoting; Ma Lili; Zhang Zhanli; Zheng Zhiming, E-mail: jiangxin@ss.buaa.edu.cn [Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing University of Aeronautics and Astronautics, 100191 Beijing (China)

    2011-01-15

    This paper presents quantum bosonic shortest path searching (QBSPS), a natural, practical and highly heuristic physical algorithm for reasoning about the recognition of network structure via quantum dynamics. QBSPS is based on an Anderson-like itinerant bosonic system in which a boson's Green function is used as a navigation pointer for one to accurately approach the terminals. QBSPS is demonstrated by rigorous mathematical and physical proofs and plenty of simulations, showing how it can be used as a greedy routing to seek the shortest path between different locations. In methodology, it is an interesting and new algorithm rooted in the quantum mechanism other than combinatorics. In practice, for the all-pairs shortest-path problem in a random scale-free network with N vertices, QBSPS runs in O({mu}(N) ln ln N) time. In application, we suggest that the corresponding experimental realizations are feasible by considering path searching in quantum optical communication networks; in this situation, the method performs a pure local search on networks without requiring the global structure that is necessary for current graph algorithms.

  16. QuVis interactive simulations: tools to support quantum mechanics instruction

    Science.gov (United States)

    Kohnle, Antje

    2015-04-01

    Quantum mechanics holds a fascination for many students, but its mathematical complexity and counterintuitive results can present major barriers. The QuVis Quantum Mechanics Visualization Project (www.st-andrews.ac.uk/physics/quvis) aims to overcome these issues through the development and evaluation of interactive simulations with accompanying activities for the learning and teaching of quantum mechanics. Over 90 simulations are now available on the QuVis website. One collection of simulations is embedded in the Institute of Physics Quantum Physics website (quantumphysics.iop.org), which consists of freely available resources for an introductory course in quantum mechanics starting from two-level systems. Simulations support model-building by reducing complexity, focusing on fundamental ideas and making the invisible visible. They promote engaged exploration, sense-making and linking of multiple representations, and include high levels of interactivity and direct feedback. Simulations are research-based and evaluation with students informs all stages of the development process. Simulations are iteratively refined using student feedback in individual observation sessions and in-class trials. Evaluation has shown that the simulations can help students learn quantum mechanics concepts at both the introductory and advanced undergraduate level and that students perceive simulations to be beneficial to their learning. Recent activity includes the launch of a new collection of HTML5 simulations that run on both desktop and tablet-based devices and the introduction of a goal and reward structure in simulations through the inclusion of challenges. This presentation will give an overview of the QuVis resources, highlight recent work and outline future plans. QuVis is supported by the UK Institute of Physics, the UK Higher Education Academy and the University of St Andrews.

  17. Advanced quantum mechanics materials and photons

    CERN Document Server

    Dick, Rainer

    2016-01-01

    In this updated and expanded second edition of a well-received and invaluable textbook, Prof. Dick emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. Advanced Quantum Mechanics, Materials and Photons can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. This second edition includes an additional 62 new problems as well as expanded sections on relativistic quantum fields and applications of�...

  18. Wilson loops, instantons and quantum mechanics

    International Nuclear Information System (INIS)

    Schiereck, Marc

    2014-05-01

    In this thesis we examine two different problems. The first is the computation of vacuum expectation values of Wilson loop operators in ABJM theory, the other problem is finding the instanton series of the refined topological string on certain local Calabi-Yau geometries in the Nekrasov-Shatashvili limit. Based on the description of ABJM theory as a matrix model, it is possible to find a description of it in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. The vacuum-expectation-values of Wilson loop operators in ABJM theory correspond to averages of operators in the statistical-mechanical problem. Using the WKB expansion, it is possible to extract the full 1/N expansion of the vevs, up to exponentially small contributions, for arbitrary Chern-Simons coupling. We compute these vevs for the 1/6 and 1/2 BPS Wilson loops at any winding number. These can be written in terms of the Airy function. The expressions we found reproduce the low genus results previously obtained in the 't Hooft expansion. In another problem we use mirror symmetry, quantum geometry and modularity properties of elliptic curves to calculate the refined free energies, given in terms of an instanton sum, in the Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on del Pezzo surfaces. Quantum geometry here is to be understood as a quantum deformed version of rigid special geometry, which has its origin in the quantum mechanical behavior of branes in the topological string B-model. We argue that in the Seiberg-Witten picture only the Coulomb parameters lead to quantum corrections, while the mass parameters remain uncorrected. In certain cases we also compute the expansion of the free energies at the orbifold point and the conifold locus. We compute the quantum corrections order by order on ℎ by deriving second order differential operators, which act on the classical periods.

  19. How to understand quantum mechanics

    CERN Document Server

    Ralston, John P

    2018-01-01

    How to Understand Quantum Mechanics presents an accessible introduction to understanding quantum mechanics in a natural and intuitive way, which was advocated by Erwin Schroedinger and Albert Einstein. A theoretical physicist reveals dozens of easy tricks that avoid long calculations, makes complicated things simple, and bypasses the worthless anguish of famous scientists who died in angst. The author's approach is light-hearted, and the book is written to be read without equations, however all relevant equations still appear with explanations as to what they mean. The book entertainingly rejects quantum disinformation, the MKS unit system (obsolete), pompous non-explanations, pompous people, the hoax of the 'uncertainty principle' (it is just a math relation), and the accumulated junk-DNA that got into the quantum operating system by misreporting it. The order of presentation is new and also unique by warning about traps to be avoided, while separating topics such as quantum probability to let the Schroeding...

  20. Mind, matter and quantum mechanics

    CERN Document Server

    Stapp, Henry P

    2009-01-01

    "Scientists other than quantum physicists often fail to comprehend the enormity of the conceptual change wrought by quantum theory in our basic conception of the nature of matter," writes Henry Stapp. Stapp is a leading quantum physicist who has given particularly careful thought to the implications of the theory that lies at the heart of modern physics. In this book, which contains several of his key papers as well as new material, he focuses on the problem of consciousness and explains how quantum mechanics allows causally effective conscious thought to be combined in a natural way with the physical brain made of neurons and atoms. The book is divided into four sections. The first consists of an extended introduction. Key foundational and somewhat more technical papers are included in the second part, together with a clear exposition of the "orthodox" interpretation of quantum mechanics. The third part addresses, in a non-technical fashion, the implications of the theory for some of the most profound questi...

  1. Mathematics and quantum mechanics

    International Nuclear Information System (INIS)

    Santander, M.

    2000-01-01

    Several episodes in the relation between Mathematics and Quantum Mechanics are discussed; and the emphasis is put in the existence of multiple and sometimes unexpected connections between ideas originating in Mathematics and in Quantum Physics. The question of the unresasonable effectiveness of Mathematics in Physics is also presented in the same light. (Author) 3 refs

  2. Exploring the boundaries of quantum mechanics: advances in satellite quantum communications.

    Science.gov (United States)

    Agnesi, Costantino; Vedovato, Francesco; Schiavon, Matteo; Dequal, Daniele; Calderaro, Luca; Tomasin, Marco; Marangon, Davide G; Stanco, Andrea; Luceri, Vincenza; Bianco, Giuseppe; Vallone, Giuseppe; Villoresi, Paolo

    2018-07-13

    Recent interest in quantum communications has stimulated great technological progress in satellite quantum technologies. These advances have rendered the aforesaid technologies mature enough to support the realization of experiments that test the foundations of quantum theory at unprecedented scales and in the unexplored space environment. Such experiments, in fact, could explore the boundaries of quantum theory and may provide new insights to investigate phenomena where gravity affects quantum objects. Here, we review recent results in satellite quantum communications and discuss possible phenomena that could be observable with current technologies. Furthermore, stressing the fact that space represents an incredible resource to realize new experiments aimed at highlighting some physical effects, we challenge the community to propose new experiments that unveil the interplay between quantum mechanics and gravity that could be realizable in the near future.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

  3. Toward a microrealistic version of quantum mechanics. II

    International Nuclear Information System (INIS)

    Maxwell, N.

    1976-01-01

    Possible objections to the propensity microrealistic version of quantum mechanics proposed previously are answered. This version of quantum mechanics is compared with the statistical, particle, microrealistic viewpoint, and a crucial experiment is proposed designed to distinguish between these two microrealistic versions of quantum mechanics

  4. Macro-mechanics controls quantum mechanics: mechanically controllable quantum conductance switching of an electrochemically fabricated atomic-scale point contact.

    Science.gov (United States)

    Staiger, Torben; Wertz, Florian; Xie, Fangqing; Heinze, Marcel; Schmieder, Philipp; Lutzweiler, Christian; Schimmel, Thomas

    2018-01-12

    Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from 'electrochemical' to 'mechanical', which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.

  5. Mind, Matter and Quantum Mechanics (2nd edition)

    Energy Technology Data Exchange (ETDEWEB)

    Mahler, G [Institute of Theoretical Physics, Universitaet Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart (Germany)

    2004-07-02

    Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the 'principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or 'complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a 'higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space - not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on 'instantaneous' projections within some externally selected measurement basis. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, 'implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their

  6. Nonlocality and localizability in quantum mechanics

    International Nuclear Information System (INIS)

    Matsuno, K.

    1989-01-01

    Nonlocality of simultaneous spatial correlation of a quantum phenomenon as demonstrated in various versions of Einstein-Podolsky-Rosen type experiment reduces to nonlocality of the measurement apparatus in the sense that the eigen-wavefunctions for the apparatus are completely specified in a manner of being independent of whatever object it may measure. Nonlocality of the measurement apparatus however serves as no more than a good approximation to reality at best. The theoretical imposition of nonlocality of the measurement apparatus as an approximation is compatible with the actual locality of quantum mechanics that dispenses with an agent claiming globally simultaneous specifiability of boundary conditions, though the genuine locality of quantum mechanics has to be examined without employing the nonlocality of the measurement apparatus. The actual locality of quantum mechanics is intrinsically irreversible in its development

  7. Introduction to quantum mechanics a time-dependent perspective

    CERN Document Server

    Tannor, David J

    2007-01-01

    "Introduction to Quantum Mechanics" covers quantum mechanics from a time-dependent perspective in a unified way from beginning to end. Intended for upper-level undergraduate and graduate courses this text will change the way people think about and teach quantum mechanics in chemistry and physics departments.

  8. Framework for understanding the patterns of student difficulties in quantum mechanics

    Directory of Open Access Journals (Sweden)

    Emily Marshman

    2015-09-01

    Full Text Available [This paper is part of the Focused Collection on Upper Division Physics Courses.] Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing expertise in quantum mechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates both the effects of diversity in upper-level students’ prior preparation, goals, and motivation in general (i.e., the facts that even in upper-level courses, students may be inadequately prepared, have unclear goals, and have insufficient motivation to excel as well as the “paradigm shift” from classical mechanics to quantum mechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantum mechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantum mechanics and introductory classical mechanics are discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantum mechanics.

  9. Framework for understanding the patterns of student difficulties in quantum mechanics

    Science.gov (United States)

    Marshman, Emily; Singh, Chandralekha

    2015-12-01

    [This paper is part of the Focused Collection on Upper Division Physics Courses.] Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. Here, we describe a framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing expertise in quantum mechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates both the effects of diversity in upper-level students' prior preparation, goals, and motivation in general (i.e., the facts that even in upper-level courses, students may be inadequately prepared, have unclear goals, and have insufficient motivation to excel) as well as the "paradigm shift" from classical mechanics to quantum mechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantum mechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantum mechanics and introductory classical mechanics are discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantum mechanics.

  10. Quantum mechanics a comprehensive text for chemistry

    CERN Document Server

    Arora, Kishor

    2010-01-01

    This book contains 14 chapters. The text includes the inadequacy of classical mechanics and covers basic and fundamental concepts of quantum mechanics including concepts of transitional, vibration rotation and electronic energies, introduction to concepts of angular momenta, approximatemethods and their application concepts related to electron spin, symmetery concepts and quantum mechanics and ultimately the book features the theories of chemical bonding and use of softwares in quantum mechanics. the text of the book is presented in a lucid manner with ample examples and illustrations wherever

  11. The transactional interpretation of quantum mechanics

    Science.gov (United States)

    Cramer, John G.

    2001-06-01

    The transactional interpretation of quantum mechanics [1] was originally published in 1986 and is now about 14 years old. It is an explicitly nonlocal and Lorentz invariant alternative to the Copenhagen interpretation. It interprets the formalism for a quantum interaction as describing a "handshake" between retarded waves (ψ) and advanced waves (ψ*) for each quantum event or "transaction" in which energy, momentum, angular momentum, and other conserved quantities are transferred. The transactional interpretation offers the advantages that (1) it is actually "visible" in the formalism of quantum mechanics, (2) it is economical, involving fewer independent assumptions than its rivals, (3) it is paradox-free, resolving all of the paradoxes of standard quantum theory including nonlocality and wave function collapse, (4) it does not give a privileged role to observers or measurements, and (5) it permits the visualization of quantum events. We will review the transactional interpretation and some of its applications to "quantum paradoxes."

  12. Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Facchi, Paolo [Dipartimento di Matematica, Universita di Bari, I-70125 Bari (Italy); INFN, Sezione di Bari, I-70126 Bari (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Kulkarni, Ravi [Vivekananda Yoga Research Foundation, Bangalore 560 080 (India); Man' ko, V.I., E-mail: manko@na.infn.i [P.N. Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991 (Russian Federation); Marmo, Giuseppe [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy); Sudarshan, E.C.G. [Department of Physics, University of Texas, Austin, TX 78712 (United States); Ventriglia, Franco [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , I-80126 Napoli (Italy); INFN, Sezione di Napoli, I-80126 Napoli (Italy); MECENAS, Universita Federico II di Napoli and Universita di Bari (Italy)

    2010-11-01

    The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

  13. Classical and quantum Fisher information in the geometrical formulation of quantum mechanics

    International Nuclear Information System (INIS)

    Facchi, Paolo; Kulkarni, Ravi; Man'ko, V.I.; Marmo, Giuseppe; Sudarshan, E.C.G.; Ventriglia, Franco

    2010-01-01

    The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.

  14. A Framework for Understanding the Patterns of Student Difficulties in Quantum Mechanics

    Science.gov (United States)

    Singh, Chandralekha

    2015-04-01

    Compared with introductory physics, relatively little is known about the development of expertise in advanced physics courses, especially in the case of quantum mechanics. We describe a theoretical framework for understanding the patterns of student reasoning difficulties and how students develop expertise in quantum mechanics. The framework posits that the challenges many students face in developing expertise in quantum mechanics are analogous to the challenges introductory students face in developing expertise in introductory classical mechanics. This framework incorporates the effects of diversity in students' prior preparation, goals and motivation for taking upper-level physics courses in general as well as the ``paradigm shift'' from classical mechanics to quantum mechanics. The framework is based on empirical investigations demonstrating that the patterns of reasoning, problem-solving, and self-monitoring difficulties in quantum mechanics bear a striking resemblance to those found in introductory classical mechanics. Examples from research in quantum mechanics and introductory classical mechanics will be discussed to illustrate how the patterns of difficulties are analogous as students learn to unpack the respective principles and grasp the formalism in each knowledge domain during the development of expertise. Embracing such a theoretical framework and contemplating the parallels between the difficulties in these two knowledge domains can enable researchers to leverage the extensive literature for introductory physics education research to guide the design of teaching and learning tools for helping students develop expertise in quantum mechanics. Support from the National Science Foundation is gratefully acknowledged.

  15. The equivalence principle in classical mechanics and quantum mechanics

    OpenAIRE

    Mannheim, Philip D.

    1998-01-01

    We discuss our understanding of the equivalence principle in both classical mechanics and quantum mechanics. We show that not only does the equivalence principle hold for the trajectories of quantum particles in a background gravitational field, but also that it is only because of this that the equivalence principle is even to be expected to hold for classical particles at all.

  16. A 'general boundary' formulation for quantum mechanics and quantum gravity

    International Nuclear Information System (INIS)

    Oeckl, Robert

    2003-01-01

    I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such 'general boundary' quantum theories through a generalized path integral quantization. I show how both, non-relativistic quantum mechanics and quantum field theory can be given a 'general boundary' formulation. Surprisingly, even in the non-relativistic case, features normally associated with quantum field theory emerge from consistency conditions. This includes states with arbitrary particle number and pair creation. I also note how three-dimensional quantum gravity is an example for a realization of both proposals and suggest to apply them to four-dimensional quantum gravity

  17. A Quantum Proxy Weak Blind Signature Scheme Based on Controlled Quantum Teleportation

    Science.gov (United States)

    Cao, Hai-Jing; Yu, Yao-Feng; Song, Qin; Gao, Lan-Xiang

    2015-04-01

    Proxy blind signature is applied to the electronic paying system, electronic voting system, mobile agent system, security of internet, etc. A quantum proxy weak blind signature scheme is proposed in this paper. It is based on controlled quantum teleportation. Five-qubit entangled state functions as quantum channel. The scheme uses the physical characteristics of quantum mechanics to implement message blinding, so it could guarantee not only the unconditional security of the scheme but also the anonymity of the messages owner.

  18. Extracontextuality and extravalence in quantum mechanics.

    Science.gov (United States)

    Auffèves, Alexia; Grangier, Philippe

    2018-07-13

    We develop the point of view where quantum mechanics results from the interplay between the quantized number of 'modalities' accessible to a quantum system, and the continuum of 'contexts' that are required to define these modalities. We point out the specific roles of 'extracontextuality' and 'extravalence' of modalities, and relate them to the Kochen-Specker and Gleason theorems.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

  19. Entropy, Topological Theories and Emergent Quantum Mechanics

    Directory of Open Access Journals (Sweden)

    D. Cabrera

    2017-02-01

    Full Text Available The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a finite dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.

  20. Mathematical concepts of quantum mechanics. 2. ed.

    International Nuclear Information System (INIS)

    Gustafson, Stephen J.; Sigal, Israel Michael

    2011-01-01

    The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory. (orig.)

  1. Theoretical and quantum mechanics fundamentals for chemists

    CERN Document Server

    Ivanov, Stefan

    2006-01-01

    Provides the basics of theoretical and quantum mechanics in one place and emphasizes the continuity between themUniquely presented to be used for self-taught courses covering theoretical and quantum mechanicsEach chapter includes a detailed outline, a summary, self-assessment questions for which answers can be found in the textInvaluable for chemistry undergraduate and graduate students, chemists, other non-physical scientists, engineering students of modern techniques and technology, specialists who need a better understanding of quantum mechanics.

  2. Communication: Quantum mechanics without wavefunctions

    Energy Technology Data Exchange (ETDEWEB)

    Schiff, Jeremy [Department of Mathematics, Bar-Ilan University, Ramat Gan 52900 (Israel); Poirier, Bill [Department of Chemistry and Biochemistry, Texas Tech University, Box 41061, Lubbock, Texas 79409-1061 (United States) and Department of Physics, Texas Tech University, Box 41051, Lubbock, Texas 79409-1051 (United States)

    2012-01-21

    We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.

  3. Communication: Quantum mechanics without wavefunctions

    International Nuclear Information System (INIS)

    Schiff, Jeremy; Poirier, Bill

    2012-01-01

    We present a self-contained formulation of spin-free non-relativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications--theoretical, computational, and interpretational--are discussed.

  4. Lectures on Quantum Mechanics

    Science.gov (United States)

    Weinberg, Steven

    2015-09-01

    Preface; Notation; 1. Historical introduction; 2. Particle states in a central potential; 3. General principles of quantum mechanics; 4. Spin; 5. Approximations for energy eigenstates; 6. Approximations for time-dependent problems; 7. Potential scattering; 8. General scattering theory; 9. The canonical formalism; 10. Charged particles in electromagnetic fields; 11. The quantum theory of radiation; 12. Entanglement; Author index; Subject index.

  5. Theoretical physics 3. Quantum mechanics 1 with problems in MAPLE

    International Nuclear Information System (INIS)

    Reineker, P.; Schulz, M.; Schulz, B.M.

    2007-01-01

    The following topics are dealt with: Historically heuristic introduction to quantum mechanics, the Schroedinger equation, foundations of quantum mechanics, the linear harmonic oscillator, quantum-mechanical motion in the central field, approximation methods for the solution of quantum mechanical problems, motion of particles in the electromagnetic field, spin and magnetic moment of the electron, many-particle systems, conceptional problems of quantum mechanics

  6. Stochastic methods in quantum mechanics

    CERN Document Server

    Gudder, Stanley P

    2005-01-01

    Practical developments in such fields as optical coherence, communication engineering, and laser technology have developed from the applications of stochastic methods. This introductory survey offers a broad view of some of the most useful stochastic methods and techniques in quantum physics, functional analysis, probability theory, communications, and electrical engineering. Starting with a history of quantum mechanics, it examines both the quantum logic approach and the operational approach, with explorations of random fields and quantum field theory.The text assumes a basic knowledge of fun

  7. Mathematical methods in quantum and statistical mechanics

    International Nuclear Information System (INIS)

    Fishman, L.

    1977-01-01

    The mathematical structure and closed-form solutions pertaining to several physical problems in quantum and statistical mechanics are examined in some detail. The J-matrix method, introduced previously for s-wave scattering and based upon well-established Hilbert Space theory and related generalized integral transformation techniques, is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L 2 ), Laguerre (Slater), and oscillator (Gaussian) basis sets. The theory of relaxation in statistical mechanics within the context of the theory of linear integro-differential equations of the Master Equation type and their corresponding Markov processes is examined. Several topics of a mathematical nature concerning various computational aspects of the L 2 approach to quantum scattering theory are discussed

  8. Quantum mechanics and dynamics in phase space

    International Nuclear Information System (INIS)

    Zlatev, I.S.

    1979-01-01

    Attention is paid to formal similarity of quantum mechanics and classical statistical physics. It is supposed that quantum mechanics can be reformulated by means of the quasiprobabilistic distributions (QPD). The procedure of finding a possible dynamics of representative points in a phase space is described. This procedure would lead to an equation of the Liouville type for the given QPD. It is shown that there is always a dynamics for which the phase volume is preserved and there is another dynamics for which the equations of motion are ''canonical''. It follows from the paper that in terms of the QPD the quantum mechanics is analogous to the classical statistical mechanics and it can be interpreted as statistics of phase points, their motion obeying the canonical equations. The difference consists in the fact that in the classical statistical physics constructed is statistics of points in a phase space which depict real, existing, observable states of the system under consideration. In the quantum mechanics constructed is statistics of points in a phase space which correspond to the ''substrate'' of quantum-mechanical objects which have no any physical sense and cannot be observed separately

  9. Simple example of definitions of truth, validity, consistency, and completeness in quantum mechanics

    International Nuclear Information System (INIS)

    Benioff, P.

    1999-01-01

    Besides their use for efficient computation, quantum computers and quantum robots form a base for studying quantum systems that create valid physical theories using mathematics and physics. If quantum mechanics is universally applicable, then quantum mechanics must describe its own validation by these quantum systems. An essential part of this process is the development of a coherent theory of mathematics and quantum-mechanics together. It is expected that such a theory will include a coherent combination of mathematical logical concepts with quantum mechanics. That this might be possible is shown here by defining truth, validity, consistency, and completeness for a quantum-mechanical version of a simple (classical) expression enumeration machine described by Smullyan. Some of the expressions are chosen as sentences denoting the presence or absence of other expressions in the enumeration. Two of the sentences are self-referential. It is seen that, for an interpretation based on a Feynman path sum over expression paths, truth, consistency, and completeness for the quantum system have different properties than for the classical system. For instance, the truth of a sentence S is defined only on those paths containing S. It is undefined elsewhere. Also S and its negation can both be true provided they appear on separate paths. This satisfies the definition of consistency. The definitions of validity and completeness connect the dynamics of the system to the truth of the sentences. It is proved that validity implies consistency. It is seen that the requirements of validity and maximal completeness strongly restrict the allowable dynamics for the quantum system. Aspects of the existence of a valid, maximally complete dynamics are discussed. An exponentially efficient quantum computer is described that is also valid and complete for the set of sentences considered here. copyright 1999 The American Physical Society

  10. Extension of PT-symmetric quantum mechanics to quantum field theory with cubic interaction

    International Nuclear Information System (INIS)

    Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.

    2004-01-01

    It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition to calculate C is cumbersome in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method is used to calculate the C operator in quantum field theory. The C operator is a time-independent observable in PT-symmetric quantum field theory

  11. Pseudospectra in non-Hermitian quantum mechanics

    Science.gov (United States)

    Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

    2015-10-01

    We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

  12. On quantum mechanics for macroscopic systems

    International Nuclear Information System (INIS)

    Primas, H.

    1992-01-01

    The parable of Schroedinger's cat may lead to several up-to date questions: how to treat open systems in quantum theory, how to treat thermodynamically irreversible processes in the quantum mechanics framework, how to explain, following the quantum theory, the existence, phenomenologically evident, of classical observables, what implies the predicted existence by the quantum theory of non localized macroscopic material object ?

  13. New progress of fundamental aspects in quantum mechanics

    International Nuclear Information System (INIS)

    Sun Changpu

    2001-01-01

    The review recalls the conceptual origins of various interpretations of quantum mechanics. With the focus on quantum measurement problems, new developments of fundamental quantum theory are described in association with recent experiments such as the decoherence process in cavity quantum electrodynamics 'which-way' detection using the Bragg scattering of cold atoms, and quantum interference using the small quantum system of molecular C 60 . The fundamental problems include the quantum coherence of a macroscopic object, the von Neumann chain in quantum measurement, the Schroedinger cat paradox, et al. Many land math experiments have been accomplished with possible important applications in quantum information. The most recent research on the new quantum theory by G.'t Hooft is reviewed, as well as future prospects of quantum mechanics

  14. Quantum Backaction Evading Measurement of Collective Mechanical Modes.

    Science.gov (United States)

    Ockeloen-Korppi, C F; Damskägg, E; Pirkkalainen, J-M; Clerk, A A; Woolley, M J; Sillanpää, M A

    2016-09-30

    The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum backaction of the measurement. However, a measurement of only a single quadrature of the oscillator can evade the backaction and be made with arbitrary precision. Here we demonstrate quantum backaction evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.

  15. Testing quantum mechanics using third-order correlations

    International Nuclear Information System (INIS)

    Kinsler, P.

    1996-01-01

    Semiclassical theories similar to stochastic electrodynamics are widely used in optics. The distinguishing feature of such theories is that the quantum uncertainty is represented by random statistical fluctuations. They can successfully predict some quantum-mechanical phenomena; for example, the squeezing of the quantum uncertainty in the parametric oscillator. However, since such theories are not equivalent to quantum mechanics, they will not always be useful. Complex number representations can be used to exactly model the quantum uncertainty, but care has to be taken that approximations do not reduce the description to a hidden variable one. This paper helps show the limitations of open-quote open-quote semiclassical theories,close-quote close-quote and helps show where a true quantum-mechanical treatment needs to be used. Third-order correlations are a test that provides a clear distinction between quantum and hidden variable theories in a way analogous to that provided by the open-quote open-quote all or nothing close-quote close-quote Greenberger-Horne-Zeilinger test of local hidden variable theories. copyright 1996 The American Physical Society

  16. Deformation quantization of noncommutative quantum mechanics and dissipation

    Energy Technology Data Exchange (ETDEWEB)

    Bastos, C [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Bertolami, O [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Dias, N C [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal); Prata, J N [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal)

    2007-05-15

    We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a *-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.

  17. On the distribution functions in the quantum mechanics and Wigner functions

    International Nuclear Information System (INIS)

    Kuz'menkov, L.S.; Maksimov, S.G.

    2002-01-01

    The problem on the distribution functions, leading to the similar local values of the particles number, pulse and energy, as in the quantum mechanics, is formulated and solved. The method is based on the quantum-mechanical determination of the probability density. The derived distribution function coincides with the Wigner function only for the spatial-homogeneous systems. The Bogolyubov equations chain, the Liouville equation for the distribution quantum functions by any number of particles in the system, the general expression for the tensor of the dielectric permittivity of the plasma electron component are obtained [ru

  18. On the hypothesis that quantum mechanism manifests classical mechanics: Numerical approach to the correspondence in search of quantum chaos

    International Nuclear Information System (INIS)

    Lee, Sang-Bong.

    1993-09-01

    Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover's and Kubo-Fox-Keizer's approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty

  19. Coherent states in quantum mechanics

    CERN Document Server

    Rodrigues, R D L; Fernandes, D

    2001-01-01

    We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out.

  20. Polymer quantum mechanics and its continuum limit

    International Nuclear Information System (INIS)

    Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A.

    2007-01-01

    A rather nonstandard quantum representation of the canonical commutation relations of quantum mechanics systems, known as the polymer representation, has gained some attention in recent years, due to its possible relation with Planck scale physics. In particular, this approach has been followed in a symmetric sector of loop quantum gravity known as loop quantum cosmology. Here we explore different aspects of the relation between the ordinary Schroedinger theory and the polymer description. The paper has two parts. In the first one, we derive the polymer quantum mechanics starting from the ordinary Schroedinger theory and show that the polymer description arises as an appropriate limit. In the second part we consider the continuum limit of this theory, namely, the reverse process in which one starts from the discrete theory and tries to recover back the ordinary Schroedinger quantum mechanics. We consider several examples of interest, including the harmonic oscillator, the free particle, and a simple cosmological model

  1. Decoherence in quantum mechanics and quantum cosmology

    Science.gov (United States)

    Hartle, James B.

    1992-01-01

    A sketch of the quantum mechanics for closed systems adequate for cosmology is presented. This framework is an extension and clarification of that of Everett and builds on several aspects of the post-Everett development. It especially builds on the work of Zeh, Zurek, Joos and Zeh, and others on the interactions of quantum systems with the larger universe and on the ideas of Griffiths, Omnes, and others on the requirements for consistent probabilities of histories.

  2. ''Topological'' (Chern-Simons) quantum mechanics

    International Nuclear Information System (INIS)

    Dunne, G.V.; Jackiw, R.; Trugenberger, C.A.

    1990-01-01

    We construct quantum-mechanical models that are analogs of three-dimensional, topologically massive as well as Chern-Simons gauge-field theories, and we study the phase-space reductive limiting procedure that takes the former to the latter. The zero-point spectra of operators behave discontinuously in the limit, as a consequence of a nonperturbative quantum-mechanical anomaly. The nature of the limit for wave functions depends on the representation, but is always such that normalization is preserved

  3. Phase space quantum mechanics and maximal acceleration

    International Nuclear Information System (INIS)

    Caianiello, E.

    1989-01-01

    My presentation is a synopsis of work done since 1979 in search of connections among information theory, systems theory, quantum mechanics and other matters. The aim was 'to extract geometry from quantum mechanics'. (orig./HSI)

  4. Quantum Mechanics/Molecular Mechanics Study of the Sialyltransferase Reaction Mechanism.

    Science.gov (United States)

    Hamada, Yojiro; Kanematsu, Yusuke; Tachikawa, Masanori

    2016-10-11

    The sialyltransferase is an enzyme that transfers the sialic acid moiety from cytidine 5'-monophospho-N-acetyl-neuraminic acid (CMP-NeuAc) to the terminal position of glycans. To elucidate the catalytic mechanism of sialyltransferase, we explored the potential energy surface along the sialic acid transfer reaction coordinates by the hybrid quantum mechanics/molecular mechanics method on the basis of the crystal structure of sialyltransferase CstII. Our calculation demonstrated that CstII employed an S N 1-like reaction mechanism via the formation of a short-lived oxocarbenium ion intermediate. The computational barrier height was 19.5 kcal/mol, which reasonably corresponded with the experimental reaction rate. We also found that two tyrosine residues (Tyr156 and Tyr162) played a vital role in stabilizing the intermediate and the transition states by quantum mechanical interaction with CMP.

  5. Zeno dynamics in quantum statistical mechanics

    International Nuclear Information System (INIS)

    Schmidt, Andreas U

    2003-01-01

    We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium

  6. Physics: quantum mechanics

    International Nuclear Information System (INIS)

    Basdevant, J.L.

    1983-01-01

    This book is the second part of the physic lectures on quantum mechanics from Ecole Polytechnique. It contains some physic complements a little more thoroughly studied, mathematical complements to which refer, and an exercise and problem collection [fr

  7. Axiomation of quantum mechanics

    International Nuclear Information System (INIS)

    Kotecky, R.

    1975-01-01

    Deeper understanding of the basic structure of the formalism of the modern quantum theory (as has been established during its 50 years' stormy development) has been brought about by its axiomatization - by founding the formalism merely on experimentally directly accountable postulates without referring to historical development, without any a priori nonessential or empirically nonexplicable assumptions. A summary is given of the common formalism of quantum mechanics and its most significant axiomatizations. The assumptions are discussed under which respective axiomatically described abstract structures may be modelled by means of the common formalisn of quantum theory (established on the theory of Hilbert spaces). (author)

  8. Macro-mechanics controls quantum mechanics: mechanically controllable quantum conductance switching of an electrochemically fabricated atomic-scale point contact

    Science.gov (United States)

    Staiger, Torben; Wertz, Florian; Xie, Fangqing; Heinze, Marcel; Schmieder, Philipp; Lutzweiler, Christian; Schimmel, Thomas

    2018-01-01

    Here, we present a silver atomic-scale device fabricated and operated by a combined technique of electrochemical control (EC) and mechanically controllable break junction (MCBJ). With this EC-MCBJ technique, we can perform mechanically controllable bistable quantum conductance switching of a silver quantum point contact (QPC) in an electrochemical environment at room temperature. Furthermore, the silver QPC of the device can be controlled both mechanically and electrochemically, and the operating mode can be changed from ‘electrochemical’ to ‘mechanical’, which expands the operating mode for controlling QPCs. These experimental results offer the perspective that a silver QPC may be used as a contact for a nanoelectromechanical relay.

  9. Examples of pseudo-bosons in quantum mechanics

    International Nuclear Information System (INIS)

    Bagarello, F.

    2010-01-01

    We discuss two physical examples of the so-called pseudo-bosons, recently introduced in connection with pseudo-hermitian quantum mechanics. In particular, we show that the so-called extended harmonic oscillator and the Swanson model satisfy all the assumptions of the pseudo-bosonic framework introduced by the author. We also prove that the biorthogonal bases they produce are not Riesz bases.

  10. Entanglement, information, and the interpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Jaeger, Gregg

    2009-01-01

    This book explores the nature of quantum entanglement and quantum information and their role in the quantum world. Their relations to a number of key experiments and thought experiments in the history of quantum physics are considered, as is a range of interpretations of quantum mechanics that have been put forward as a means of understanding the fundamental nature of microphysics - the traditionally accepted domain of quantum mechanics - and in some cases, the universe as a whole. In this way, the book reveals the deep significance of entanglement and quantum information for our understanding of the physical world. (orig.)

  11. Path Integrals in Quantum Mechanics

    International Nuclear Information System (INIS)

    Chetouani, L

    2005-01-01

    By treating path integrals the author, in this book, places at the disposal of the reader a modern tool for the comprehension of standard quantum mechanics. Thus the most important applications, such as the tunnel effect, the diffusion matrix, etc, are presented from an original point of view on the action S of classical mechanics while having it play a central role in quantum mechanics. What also emerges is that the path integral describes these applications more richly than are described traditionally by differential equations, and consequently explains them more fully. The book is certainly of high quality in all aspects: original in presentation, rigorous in the demonstrations, judicious in the choice of exercises and, finally, modern, for example in the treatment of the tunnel effect by the method of instantons. Moreover, the correspondence that exists between classical and quantum mechanics is well underlined. I thus highly recommend this book (the French version being already available) to those who wish to familiarize themselves with formulation by path integrals. They will find, in addition, interesting topics suitable for exploring further. (book review)

  12. The emergent Copenhagen interpretation of quantum mechanics

    Science.gov (United States)

    Hollowood, Timothy J.

    2014-05-01

    We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.

  13. The emergent Copenhagen interpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Hollowood, Timothy J

    2014-01-01

    We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. This interpretation describes a world in which definite measurement results are obtained with probabilities that reproduce the Born rule. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR–Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems. (paper)

  14. Quantum Mechanical Balance Equation Approach to Semiconductor Device Simulation

    National Research Council Canada - National Science Library

    Cui, Long

    1997-01-01

    This research project was focused on the development of a quantum mechanical balance equation based device simulator that can model advanced, compound, submicron devices, under all transport conditions...

  15. A mechanical wave system to show waveforms similar to quantum mechanical wavefunctions in a potential

    International Nuclear Information System (INIS)

    Faletič, Sergej

    2015-01-01

    Interviews with students suggest that even though they understand the formalism and the formal nature of quantum theory, they still often desire a mental picture of what the equations describe and some tangible experience with the wavefunctions. Here we discuss a mechanical wave system capable of reproducing correctly a mechanical equivalent of a quantum system in a potential, and the resulting waveforms in principle of any form. We have successfully reproduced the finite potential well, the potential barrier and the parabolic potential. We believe that these mechanical waveforms can provide a valuable experience base for introductory students to start from. We aim to show that mechanical systems that are described with the same mathematics as quantum mechanical, indeed behave in the same way. We believe that even if treated purely as a wave phenomenon, the system provides much insight into wave mechanics. This can be especially useful for physics teachers and others who often need to resort to concepts and experience rather than mathematics when explaining physical phenomena. (paper)

  16. New developments in quantum mechanics

    CERN Document Server

    Aharonov, Yakir

    1994-01-01

    After a general introduction, some new developments on the more subtle predictions of Quantum Mechanics and their interpretation will be discussed. These include non-local topological effects, physics of pre- and post-selected quantum systems, and the question of observability of the Schrödinger wave itself.

  17. Coherent states in quantum mechanics

    International Nuclear Information System (INIS)

    Rodrigues, R. de Lima; Fernandes Junior, Damasio; Batista, Sheyla Marques

    2001-12-01

    We present a review work on the coherent states is non-relativistic quantum mechanics analysing the quantum oscillators in the coherent states. The coherent states obtained via a displacement operator that act on the wave function of ground state of the oscillator and the connection with Quantum Optics which were implemented by Glauber have also been considered. A possible generalization to the construction of new coherent states it is point out. (author)

  18. Reality, Causality, and Probability, from Quantum Mechanics to Quantum Field Theory

    Science.gov (United States)

    Plotnitsky, Arkady

    2015-10-01

    These three lectures consider the questions of reality, causality, and probability in quantum theory, from quantum mechanics to quantum field theory. They do so in part by exploring the ideas of the key founding figures of the theory, such N. Bohr, W. Heisenberg, E. Schrödinger, or P. A. M. Dirac. However, while my discussion of these figures aims to be faithful to their thinking and writings, and while these lectures are motivated by my belief in the helpfulness of their thinking for understanding and advancing quantum theory, this project is not driven by loyalty to their ideas. In part for that reason, these lectures also present different and even conflicting ways of thinking in quantum theory, such as that of Bohr or Heisenberg vs. that of Schrödinger. The lectures, most especially the third one, also consider new physical, mathematical, and philosophical complexities brought in by quantum field theory vis-à-vis quantum mechanics. I close by briefly addressing some of the implications of the argument presented here for the current state of fundamental physics.

  19. New Potentials for Old: The Darboux Transformation in Quantum Mechanics

    Science.gov (United States)

    Williams, Brian Wesley; Celius, Tevye C.

    2008-01-01

    The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…

  20. Mind, Matter and Quantum Mechanics (2nd edition)

    International Nuclear Information System (INIS)

    Mahler, G

    2004-01-01

    Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the 'principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or 'complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a 'higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space - not unlike the motion of a classical N-particle system in its 6N-dimensional phase-space. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on 'instantaneous' projections within some externally selected measurement basis. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, 'implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their possible consequences for our understanding of this world

  1. Physical aspects of pseudo-Hermitian and PT-symmetric quantum mechanics

    International Nuclear Information System (INIS)

    Mostafazadeh, Ali; Batal, Ahmet

    2004-01-01

    For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct the observables O α of the quantum mechanics based on H. In particular, we introduce pseudo-Hermitian position and momentum operators and a pseudo-Hermitian quantization scheme that relates the latter to the ordinary classical position and momentum observables. These allow us to address the problem of determining the conserved probability density and the underlying classical system for pseudo-Hermitian and in particular PT-symmetric quantum systems. As a concrete example we construct the Hermitian Hamiltonian h, the physical observables O α , the localized states and the conserved probability density for the non-Hermitian PT-symmetric square well. We achieve this by employing an appropriate perturbation scheme. For this system, we conduct a comprehensive study of both the kinematical and dynamical effects of the non-Hermiticity of the Hamiltonian on various physical quantities. In particular, we show that these effects are quantum mechanical in nature and diminish in the classical limit. Our results provide an objective assessment of the physical aspects of PT-symmetric quantum mechanics and clarify its relationship with both conventional quantum mechanics and classical mechanics

  2. Relationship between quantum walks and relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Chandrashekar, C. M.; Banerjee, Subhashish; Srikanth, R.

    2010-01-01

    Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This article revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled forms of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schroedinger form. By showing the coin to be a means to make the walk reversible and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modeled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. The Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of the quantum walk, the maximum speed of walk propagation, and earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two-state system to which the study can be extended.

  3. Quantum mechanical streamlines. I - Square potential barrier

    Science.gov (United States)

    Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

    1974-01-01

    Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

  4. Measurement and quasi-states in quantum mechanics

    International Nuclear Information System (INIS)

    Harper, C.D.

    1987-01-01

    Part of the task of quantum logic is to account for the collapse of the state vector during measurement. A difficulty in this is that it is not obvious how to describe measurement quantum mechanically as the interaction of two or more systems; interacting quantum-mechanical systems do not possess states, so their states cannot collapse. This dissertation shows that component systems of a composite system possess families of state-like vectors. These are the quasi-projections of the state vector of the composite system, each associated with a family of commutable observables. Often these quasi-projections cluster so closely around a quasi-state that they are practically indistinguishable from it. A description of measurement based on quasi-projections reveals the apparent collapse of the state vector during measurement to be illusory. The continuous evolution of the state of the composite system give rise to abrupt changes in the quasi-projections which make it appear that the state has changed. The quasi-projections cease to cluster near one quasi-state, are momentarily scattered, and then cluster again near another quasi-state. The concept of quasi-projection is also used to generalize the quantum logic of Birkhoff and von Neumann in such a fashion that a proposition can always be assigned a truth value

  5. Relativistic quantum mechanics of leptons and fields

    International Nuclear Information System (INIS)

    Grandy, W.T. Jr.

    1991-01-01

    This book serves as an advanced text on the Dirac theory, and provides a monograph summarizing the description of relativistic quantum mechanics and quantum electrodynamics as classical field theories. It presents a broad, detailed, and up-to-date exposition of relativistic quantum mechanics, including the two-body problem. It also demonstrates the extent to which the behavior of stable particles and their interactions can be understood without introducing operator (second-quantized) fields. The subsequent difficulties are studied in detail and possible resolutions are presented through quantum field theory

  6. A multiscale quantum mechanics/electromagnetics method for device simulations.

    Science.gov (United States)

    Yam, ChiYung; Meng, Lingyi; Zhang, Yu; Chen, GuanHua

    2015-04-07

    Multiscale modeling has become a popular tool for research applying to different areas including materials science, microelectronics, biology, chemistry, etc. In this tutorial review, we describe a newly developed multiscale computational method, incorporating quantum mechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantum mechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantum mechanically, while the surroundings are described by Maxwell's equations and a semiclassical drift-diffusion model. The QM model and the EM model are solved, respectively, in different regions of the system in a self-consistent manner. Potential distributions and current densities at the interface between QM and EM regions are employed as the boundary conditions for the quantum mechanical and electromagnetic simulations, respectively. The method is illustrated in the simulation of several realistic systems. In the case of junctionless field-effect transistors, transfer characteristics are obtained and a good agreement between experiments and simulations is achieved. Optical properties of a tandem photovoltaic cell are studied and the simulations demonstrate that multiple QM regions are coupled through the classical EM model. Finally, the study of a carbon nanotube-based molecular device shows the accuracy and efficiency of the QM/EM method.

  7. Optimization of a relativistic quantum mechanical engine.

    Science.gov (United States)

    Peña, Francisco J; Ferré, Michel; Orellana, P A; Rojas, René G; Vargas, P

    2016-08-01

    We present an optimal analysis for a quantum mechanical engine working between two energy baths within the framework of relativistic quantum mechanics, adopting a first-order correction. This quantum mechanical engine, with the direct energy leakage between the energy baths, consists of two adiabatic and two isoenergetic processes and uses a three-level system of two noninteracting fermions as its working substance. Assuming that the potential wall moves at a finite speed, we derive the expression of power output and, in particular, reproduce the expression for the efficiency at maximum power.

  8. Advanced quantum mechanics materials and photons

    CERN Document Server

    Dick, Rainer

    2012-01-01

    Advanced Quantum Mechanics: Materials and Photons is a textbook which emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering. Important aspects of introductory quantum mechanics are covered in the first seven chapters to make the subject self-contained and accessible for a wide audience. The textbook can therefore be used for advanced undergraduate courses and introductory graduate courses which are targeted towards students with diverse academic backgrounds from the Natural Sciences or Engineering. To enhance this inclusive aspect of making the subject as accessible as possible, Appendices A and B also provide introductions to Lagrangian mechanics and the covariant formulation of electrodynamics. Other special features include an introduction to Lagrangian field theory and an integrated discussion of transition amplitudes with discrete or continuous initial or final states. Once students have acquir...

  9. Recent developments in quantum mechanics

    International Nuclear Information System (INIS)

    Piron, C.

    1989-01-01

    It is essentially a review of recent progress in Quantum Mechanics obtained by the ''Geneva School'', put all together in a synthesis for the first time. During these twelve last years Quantum Mechanics has developed deeply in three aspects: 1) the interpretation has been completely clarified but many ''senior'' physicists delight in the mystery of their school-days Quantum Mechanics and do not want to change their minds. 2) The formalism has been developed and generalized to many (if it is not all) physical situations. 3) Many new rules of calculation have been developed. In conclusion many paradoxes and/or unsolved problems have been solved and many calculations which usually appear just as tricks can be explained and justified. I want here to give a brief survey of each one of these three points and to end by some examples which show the power and the efficiency of this new theory. (orig.)

  10. Fundamentals of quantum mechanics

    CERN Document Server

    Erkoc, Sakir

    2006-01-01

    HISTORICAL EXPERIMENTS AND THEORIESDates of Important Discoveries and Events Blackbody RadiationPhotoelectrice Effect Quantum Theory of Spectra TheComptone Effect Matterwaves, the de Broglie HypothesisThe Davisson -Germer Experiment Heisenberg's Uncertainity PrincipleDifference Between Particles and Waves Interpretation of the Wavefunction AXIOMATIC STRUCTURE OF QUANTUM MECHANICSThe Necessity of Quantum TheoryFunction Spaces Postulates of Quantum Mechanics The Kronecker Delta and the Dirac Delta Function Dirac Notation OBSERVABLES AND SUPERPOSITIONFree Particle Particle In A Box Ensemble Average Hilbert -Space Interpretation The Initial Square Wave Particle Beam Superposition and Uncertainty Degeneracy of States Commutators and Uncertainty TIME DEVELOPMENT AND CONSERVATION THEOREMSTime Development of State Functions, The Discrete Case The Continuous Case, Wave Packets Particle Beam Gaussian Wave Packet Free Particle Propagator The Limiting Cases of the Gaussian Wave Packets Time Development of Expectation Val...

  11. Fun with supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Freedman, B.; Cooper, F.

    1984-04-01

    One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup α/ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index Δ which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if Δ is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate Δ for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references

  12. Is Quantum Mechanics a Complete Theory?: A Philosophical ...

    African Journals Online (AJOL)

    In 1935, Einstein, Podolsky, and Rosen published their thought experiment I a paper entitled, “Can QuantumMechanical Description of Physical Reality be considered complete?”. At that time, Bohr, Heisenberg, and the proponents of the Copenhagen interpretation of Quantum mechanics, were saying that Quantum ...

  13. Quantum mechanical irreversibility and measurement

    CERN Document Server

    Grigolini, P

    1993-01-01

    This book is intended as a tutorial approach to some of the techniques used to deal with quantum dissipation and irreversibility, with special focus on their applications to the theory of measurements. The main purpose is to provide readers without a deep expertise in quantum statistical mechanics with the basic tools to develop a critical judgement on whether the major achievements in this field have to be considered a satisfactory solution of quantum paradox, or rather this ambitious achievement has to be postponed to when a new physics, more general than quantum and classical physics, will

  14. Quantum mechanics of history: The decoherence functional in quantum mechanics

    International Nuclear Information System (INIS)

    Dowker, H.F.; Halliwell, J.J.

    1992-01-01

    We study a formulation of quantum mechanics in which the central notion is that of a quantum-mechanical history---a sequence of events at a succession of times. The primary aim is to identify sets of ''decoherent'' (or ''consistent'') histories for the system. These are quantum-mechanical histories suffering negligible interference with each other, and, therefore, to which probabilities may be assigned. These histories may be found for a given system using the so-called decoherence functional. When the decoherence functional is exactly diagonal, probabilities may be assigned to the histories, and all probability sum rules are satisfied exactly. We propose a condition for approximate decoherence, and argue that it implies that most probability sum rules will be satisfied to approximately the same degree. We also derive an inequality bounding the size of the off-diagonal terms of the decoherence functional. We calculate the decoherence functional for some simple one-dimensional systems, with a variety of initial states. For these systems, we explore the extent to which decoherence is produced using two different types of coarse graining. The first type of coarse graining involves imprecise specification of the particle's position. The second involves coupling the particle to a thermal bath of harmonic oscillators and ignoring the details of the bath (the Caldeira-Leggett model). We argue that both types of coarse graining are necessary in general. We explicitly exhibit the degree of decoherence as a function of the temperature of the bath, and of the width to within which the particle's position is specified. We study the diagonal elements of the decoherence functional, representing the probabilities for the possible histories of the system

  15. Concepts in quantum mechanics

    CERN Document Server

    Mathur, Vishnu S

    2008-01-01

    NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS Inadequacy of Classical Description for Small Systems Basis of Quantum Mechanics Representation of States Dual Vectors: Bra and Ket Vectors Linear Operators Adjoint of a Linear Operator Eigenvalues and Eigenvectors of a Linear Operator Physical Interpretation Observables and Completeness Criterion Commutativity and Compatibility of Observables Position and Momentum Commutation Relations Commutation Relation and the Uncertainty ProductAppendix: Basic Concepts in Classical MechanicsREPRESENTATION THEORY Meaning of Representation How to Set up a Representation Representatives of a Linear Operator Change of Representation Coordinate Representation Replacement of Momentum Observable p by -ih d/dqIntegral Representation of Dirac Bracket A2|F|A1> The Momentum Representation Dirac Delta FunctionRelation between the Coordinate and Momentum RepresentationsEQUATIONS OF MOTIONSchrödinger Equation of Motion Schrödinger Equation in the Coordinate Representation Equation o...

  16. Projection quantum mechanics and neutrino mixing

    Energy Technology Data Exchange (ETDEWEB)

    Góźdź, A., E-mail: andrzej.gozdz@umcs.lublin.pl; Góźdź, M., E-mail: mgozdz@kft.umcs.lublin.pl [University of Maria Curie–Skłodowska, Faculty of Mathematics, Physics and Computer Science (Poland)

    2017-03-15

    The theory of neutrino oscillations rests on the assumption, that the interaction basis and the physical (mass) basis of neutrino states are different. Therefore neutrino is produced in a certain welldefined superposition of three mass eigenstates, which propagate separately and may be detected as a different superposition. This is called flavor oscillations. It is, however, not clear why neutrinos behave this way, i.e., what is the underlying mechanism which leads to the production of a superposition of physical states in a single reaction. In this paper we argue, that one of the reasons may be connected with the temporal structure of the process. In order to discuss the role of time in processes on the quantum level, we use a special formulation of the quantum mechanics, which is based on the projection time evolution. We arrive at the conclusion, that for short reaction times the formation of a superposition of states of similar masses is natural.

  17. On Galilean covariant quantum mechanics

    International Nuclear Information System (INIS)

    Horzela, A.; Kapuscik, E.; Kempczynski, J.; Joint Inst. for Nuclear Research, Dubna

    1991-08-01

    Formalism exhibiting the Galilean covariance of wave mechanics is proposed. A new notion of quantum mechanical forces is introduced. The formalism is illustrated on the example of the harmonic oscillator. (author)

  18. Is string interaction the origin of quantum mechanics?

    Energy Technology Data Exchange (ETDEWEB)

    Bars, Itzhak, E-mail: bars@usc.edu; Rychkov, Dmitry

    2014-12-12

    String theory was developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend that open string field theory is a fully consistent definition of the theory – it is at least a self-consistent sector. Then we find in its structure that the rules of quantum mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions. Thus, rather than assuming the quantum commutation rules among the usual canonical variables we derive them from the physical process of string interactions. Morally we could apply such an argument to M-theory to cover quantum mechanics for all physics. If string or M-theory really underlies all physics, it seems that the door has been opened to an explanation of the origins of quantum mechanics from the physical processes point of view.

  19. Probability in quantum mechanics

    Directory of Open Access Journals (Sweden)

    J. G. Gilson

    1982-01-01

    Full Text Available By using a fluid theory which is an alternative to quantum theory but from which the latter can be deduced exactly, the long-standing problem of how quantum mechanics is related to stochastic processes is studied. It can be seen how the Schrödinger probability density has a relationship to time spent on small sections of an orbit, just as the probability density has in some classical contexts.

  20. Level comparison theorems and supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Baumgartner, B.; Grosse, H.

    1986-01-01

    The sign of the Laplacian of the spherical symmetric potential determines the order of energy levels with the same principal Coulomb quantum number. This recently derived theorem has been generalized, extended and applied to various situations in particle, nuclear and atomic physics. Besides a comparison theorem the essential step was the use of supersymmetric quantum mechanics. Recently worked out applications of supersymmetric quantum mechanics to index problems of Dirac operators are mentioned. (Author)

  1. Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

    International Nuclear Information System (INIS)

    Remler, E.A.

    1977-01-01

    A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

  2. The Quantum Mechanics Solver How to Apply Quantum Theory to Modern Physics

    CERN Document Server

    Basdevant, Jean-Louis

    2006-01-01

    The Quantum Mechanics Solver grew from topics which are part of the final examination in quantum theory at the Ecole Polytechnique at Palaiseau near Paris, France. The aim of the text is to guide the student towards applying quantum mechanics to research problems in fields such as atomic and molecular physics, condensed matter physics, and laser physics. Advanced undergraduates and graduate students will find a rich and challenging source for improving their skills in this field.

  3. Improving Student Understanding of Addition of Angular Momentum in Quantum Mechanics

    Science.gov (United States)

    Zhu, Guangtian; Singh, Chandralekha

    2013-01-01

    We describe the difficulties advanced undergraduate and graduate students have with concepts related to addition of angular momentum in quantum mechanics. We also describe the development and implementation of a research-based learning tool, Quantum Interactive Learning Tutorial (QuILT), to reduce these difficulties. The preliminary evaluation…

  4. Dynamical parasupersymmetries in quantum mechanics

    International Nuclear Information System (INIS)

    Durand, S.; Vinet, L.

    1990-01-01

    This paper reports on supersymmetric field theories that have the distinctive feature of being invariant under transformations that mix bosonic and fermionic variables. Reduction to 0 + 1 dimensions yields mechanical models with an analogous invariance. In this case, the Grassmannian variables are interpreted as describing (classically) the spin degrees of freedom of the particles involved. After canonical quantization, the corresponding quantities obey the standard anticommutation relations of fermionic creation and annihilation operators. It is known that paraquantitization offers alternative to the usual quantization scheme. In this framework, one can expect that it is possible to construct parasupersymmetric theories, that is, theories which are invariant under transformations between bosonic and parafermionic variables. As a matter of fact, Rubakov and Spiridonov has recently shown how the parasupersymmetric generalization of supersymmetric Quantum Mechanics proceeds. In this case, the fermionic creation and annihilation operators obey paracommutation relations. The applications of supersymmetric Quantum Mechanics are many. One might hope that its parasupersymmetric generalization will be as useful. The elaboration of parasupersymmeric Quantum Mechanics moreover has led to new mathematical constructs; indeed, the symmetry generators realize algebras involving products of degree higher than 2

  5. Approach to measurement to quantum mechanics

    International Nuclear Information System (INIS)

    Sudarshan, E.C.G.; Sherry, T.N.; Gautam, S.R.

    1977-10-01

    An unconventional approach to the measurement problem in quantum mechanics is considered, the apparatus is treated as a classical system, belonging to the macro-world. In order to have a measurement the apparatus must interact with the quantum system. As a first step, the classical apparatus is embedded into a larger quantum mechanical structure, making use of superselection rules. Projection back to the classical system is possible. The apparatus and system are now coupled such that the apparatus remains classical (principle of integrity), and unambiguous information of the values of a quantum observable are transferred to the variables of the apparatus. Finally, projection back to the classical formulation is accomplished. Further measurement of the classical apparatus can be done, causing no problems of principle. Thus interactions causing pointers to move (which are not treat) can be added. The restrictions placed by the principle of integrity on the form of the interaction between classical and quantum systems are examined

  6. Phase space view of quantum mechanical systems and Fisher information

    Energy Technology Data Exchange (ETDEWEB)

    Nagy, Á., E-mail: anagy@madget.atomki.hu

    2016-06-17

    Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.

  7. Phase space view of quantum mechanical systems and Fisher information

    International Nuclear Information System (INIS)

    Nagy, Á.

    2016-01-01

    Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.

  8. Historical and interpretative aspects of quantum mechanics: a physicists' naive approach

    Directory of Open Access Journals (Sweden)

    B.Berche

    2006-01-01

    Full Text Available Many theoretical predictions derived from quantum mechanics have been confirmed experimentally for the last 80 years. However, interpretative aspects have long been subject to debate. Among them, the question of the existence of hidden variables is still open. We review these questions, paying special attention to historical aspects, and argue that one may definitively exclude local realism based on the present experimental outcomes. Nevertheless other interpretations of Quantum Mechanics are not excluded.

  9. General principles of quantum mechanics

    International Nuclear Information System (INIS)

    Pauli, W.

    1980-01-01

    This book is a textbook for a course in quantum mechanics. Starting from the complementarity and the uncertainty principle Schroedingers equation is introduced together with the operator calculus. Then stationary states are treated as eigenvalue problems. Furthermore matrix mechanics are briefly discussed. Thereafter the theory of measurements is considered. Then as approximation methods perturbation theory and the WKB approximation are introduced. Then identical particles, spin, and the exclusion principle are discussed. There after the semiclassical theory of radiation and the relativistic one-particle problem are discussed. Finally an introduction is given into quantum electrodynamics. (HSI)

  10. Quantum mechanical properties of graphene nano-flakes and quantum dots.

    Science.gov (United States)

    Shi, Hongqing; Barnard, Amanda S; Snook, Ian K

    2012-11-07

    In recent years considerable attention has been given to methods for modifying and controlling the electronic and quantum mechanical properties of graphene quantum dots. However, as these types of properties are indirect consequences of the wavefunction of the material, a more efficient way of determining properties may be to engineer the wavefunction directly. One way of doing this may be via deliberate structural modifications, such as producing graphene nanostructures with specific sizes and shapes. In this paper we use quantum mechanical simulations to determine whether the wavefunction, quantified via the distribution of the highest occupied molecular orbital, has a direct and reliable relationship to the physical structure, and whether structural modifications can be useful for wavefunction engineering. We find that the wavefunction of small molecular graphene structures can be different from those of larger nanoscale counterparts, and the distribution of the highest occupied molecular orbital is strongly affected by the geometric shape (but only weakly by edge and corner terminations). This indicates that both size and shape may be more useful parameters in determining quantum mechanical and electronic properties, which should then be reasonably robust against variations in the chemical passivation or functionalisation around the circumference.

  11. Faithful conversion of propagating quantum information to mechanical motion

    Science.gov (United States)

    Reed, A. P.; Mayer, K. H.; Teufel, J. D.; Burkhart, L. D.; Pfaff, W.; Reagor, M.; Sletten, L.; Ma, X.; Schoelkopf, R. J.; Knill, E.; Lehnert, K. W.

    2017-12-01

    The motion of micrometre-sized mechanical resonators can now be controlled and measured at the fundamental limits imposed by quantum mechanics. These resonators have been prepared in their motional ground state or in squeezed states, measured with quantum-limited precision, and even entangled with microwave fields. Such advances make it possible to process quantum information using the motion of a macroscopic object. In particular, recent experiments have combined mechanical resonators with superconducting quantum circuits to frequency-convert, store and amplify propagating microwave fields. But these systems have not been used to manipulate states that encode quantum bits (qubits), which are required for quantum communication and modular quantum computation. Here we demonstrate the conversion of propagating qubits encoded as superpositions of zero and one photons to the motion of a micromechanical resonator with a fidelity in excess of the classical bound. This ability is necessary for mechanical resonators to convert quantum information between the microwave and optical domains or to act as storage elements in a modular quantum information processor. Additionally, these results are an important step towards testing speculative notions that quantum theory may not be valid for sufficiently massive systems.

  12. Quantum mechanics over sets

    Science.gov (United States)

    Ellerman, David

    2014-03-01

    In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

  13. Quantum mechanics of time travel through post-selected teleportation

    International Nuclear Information System (INIS)

    Lloyd, Seth; Garcia-Patron, Raul; Maccone, Lorenzo; Giovannetti, Vittorio; Shikano, Yutaka

    2011-01-01

    This paper discusses the quantum mechanics of closed-timelike curves (CTCs) and of other potential methods for time travel. We analyze a specific proposal for such quantum time travel, the quantum description of CTCs based on post-selected teleportation (P-CTCs). We compare the theory of P-CTCs to previously proposed quantum theories of time travel: the theory is inequivalent to Deutsch's theory of CTCs, but it is consistent with path-integral approaches (which are the best suited for analyzing quantum-field theory in curved space-time). We derive the dynamical equations that a chronology-respecting system interacting with a CTC will experience. We discuss the possibility of time travel in the absence of general-relativistic closed-timelike curves, and investigate the implications of P-CTCs for enhancing the power of computation.

  14. Kowalevski top in quantum mechanics

    International Nuclear Information System (INIS)

    Matsuyama, A.

    2013-01-01

    The quantum mechanical Kowalevski top is studied by the direct diagonalization of the Hamiltonian. The spectra show different behaviors depending on the region divided by the bifurcation sets of the classical invariant tori. Some of these spectra are nearly degenerate due to the multiplicity of the invariant tori. The Kowalevski top has several symmetries and symmetry quantum numbers can be assigned to the eigenstates. We have also carried out the semiclassical quantization of the Kowalevski top by the EBK formulation. It is found that the semiclassical spectra are close to the exact values, thus the eigenstates can be also labeled by the integer quantum numbers. The symmetries of the system are shown to have close relations with the semiclassical quantum numbers and the near-degeneracy of the spectra. -- Highlights: •Quantum spectra of the Kowalevski top are calculated. •Semiclassical quantization is carried out by the EBK formulation. •Quantum states are labeled by the semiclassical integer quantum numbers. •Multiplicity of the classical torus makes the spectra nearly degenerate. •Symmetries, quantum numbers and near-degenerate spectra are closely related

  15. Lectures on Quantum Mechanics

    CERN Document Server

    Basdevant, Jean-Louis

    2007-01-01

    Beautifully illustrated and engagingly written, Lectures on Quantum Mechanics presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment. Here is a sample of the book's style, from the opening of Chapter 1: "If one were to ask a passer-by to quote a great formula of physics, chances are that the answer would be 'E = mc2'. Nevertheless, the formula 'E=hV' which was written in the same year 1905 by the same Albert Einstein, and which started quantum theory, concerns their daily life considerably more. In fact, of the three watershed years for physics toward the beginning of the 20th century - 1905: the Special Relativity of Einstein, Lorentz and Poincaré; 1915: the General Relativity of Einstein, with its extraordinary reflections on gravitation, space and time; and 1925: the full development of Quantum Mechanics - it is surely the last which has the mos...

  16. The pursuit of locality in quantum mechanics

    Science.gov (United States)

    Hodkin, Malcolm

    The rampant success of quantum theory is the result of applications of the 'new' quantum mechanics of Schrodinger and Heisenberg (1926-7), the Feynman-Schwinger-Tomonaga Quantum Electro-dynamics (1946-51), the electro-weak theory of Salaam, Weinberg, and Glashow (1967-9), and Quantum Chromodynamics (1973-); in fact, this success of 'the' quantum theory has depended on a continuous stream of brilliant and quite disparate mathematical formulations. In this carefully concealed ferment there lie plenty of unresolved difficulties, simply because in churning out fabulously accurate calculational tools there has been no sensible explanation of all that is going on. It is even argued that such an understanding is nothing to do with physics. A long-standing and famous illustration of this is the paradoxical thought-experiment of Einstein, Podolsky and Rosen (1935). Fundamental to all quantum theories, and also their paradoxes, is the location of sub-microscopic objects; or, rather, that the specification of such a location is fraught with mathematical inconsistency. This project encompasses a detailed, critical survey of the tangled history of Position within quantum theories. The first step is to show that, contrary to appearances, canonical quantum mechanics has only a vague notion of locality. After analysing a number of previous attempts at a 'relativistic quantum mechanics', two lines of thought are considered in detail. The first is the work of Wan and students, which is shown to be no real improvement on the iisu.al 'nonrelativistic' theory. The second is based on an idea of Dirac's - using backwards-in-time light-cones as the hypersurface in space-time. There remain considerable difficulties in the way of producing a consistent scheme here. To keep things nicely stirred up, the author then proposes his own approach - an adaptation of Feynman's QED propagators. This new approach is distinguished from Feynman's since the propagator or Green's function is not obtained

  17. Quantum Sensing of Mechanical Motion with a Single InAs Quantum Dot

    Science.gov (United States)

    2017-03-01

    Wenner, J. M. Martinis, and A. N. Cleland, “ Quantum ground state and single- phonon control of a mechanical resonator.,” Nature, vol. 464, no...G. Nogues, S. Seidelin, J. Poizat, O. Arcizet, and M. Richard, “Strain-mediated coupling in a quantum dot- mechanical oscillator hybrid system...Pos 4 Dep 5 School of N upling quantu ctive for funda dded a semico nical resonat vances in thi es large ch ell as the spin for quantum s antum Dots

  18. Quantum ground state and single-phonon control of a mechanical resonator.

    Science.gov (United States)

    O'Connell, A D; Hofheinz, M; Ansmann, M; Bialczak, Radoslaw C; Lenander, M; Lucero, Erik; Neeley, M; Sank, D; Wang, H; Weides, M; Wenner, J; Martinis, John M; Cleland, A N

    2010-04-01

    Quantum mechanics provides a highly accurate description of a wide variety of physical systems. However, a demonstration that quantum mechanics applies equally to macroscopic mechanical systems has been a long-standing challenge, hindered by the difficulty of cooling a mechanical mode to its quantum ground state. The temperatures required are typically far below those attainable with standard cryogenic methods, so significant effort has been devoted to developing alternative cooling techniques. Once in the ground state, quantum-limited measurements must then be demonstrated. Here, using conventional cryogenic refrigeration, we show that we can cool a mechanical mode to its quantum ground state by using a microwave-frequency mechanical oscillator-a 'quantum drum'-coupled to a quantum bit, which is used to measure the quantum state of the resonator. We further show that we can controllably create single quantum excitations (phonons) in the resonator, thus taking the first steps to complete quantum control of a mechanical system.

  19. John S. Bell on the foundations of quantum mechanics

    CERN Document Server

    Bell, John S; Gottfried, Kurt; Veltman, Martinus J G

    2001-01-01

    This book is the most complete collection of John S Bell's research papers, review articles and lecture notes on the foundations of quantum mechanics. Some of this material has hitherto been difficult to access. The book also appears in a paperback edition, aimed at students and young researchers. This volume will be very useful to researchers in the foundations and applications of quantum mechanics. Contents: (1) On the Problem of Hidden Variables in Quantum Mechanics; (2) On the Einstein-Podolsky-Rosen Paradox; (3) The Moral Aspect of Quantum Mechanics; (4) Introduction to the Hidden-Variabl

  20. Symmetry aspects in emergent quantum mechanics

    Science.gov (United States)

    Elze, Hans-Thomas

    2009-06-01

    We discuss an explicit realization of the dissipative dynamics anticipated in the proof of 't Hooft's existence theorem, which states that 'For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization'. - There is an energy-parity symmetry hidden in the Liouville equation, which mimics the Kaplan-Sundrum protective symmetry for the cosmological constant. This symmetry may be broken by the coarse-graining inherent in physics at scales much larger than the Planck length. We correspondingly modify classical ensemble theory by incorporating dissipative fluctuations (information loss) - which are caused by discrete spacetime continually 'measuring' matter. In this way, aspects of quantum mechanics, such as the von Neumann equation, including a Lindblad term, arise dynamically and expectations of observables agree with the Born rule. However, the resulting quantum coherence is accompanied by an intrinsic decoherence and continuous localization mechanism. Our proposal leads towards a theory that is linear and local at the quantum mechanical level, but the relation to the underlying classical degrees of freedom is nonlocal.

  1. Introductory quantum mechanics for semiconductor nanotechnology

    International Nuclear Information System (INIS)

    Kim, Dae Mann

    2010-01-01

    The result of the nano education project run by the Korean Nano Technology Initiative, this has been recommended for use as official textbook by the Korean Nanotechnology Research Society. The author is highly experienced in teaching both physics and engineering in academia and industry, and naturally adopts an interdisciplinary approach here. He is short on formulations but long on applications, allowing students to understand the essential workings of quantum mechanics without spending too much time covering the wide realms of physics. He takes care to provide sufficient technical background and motivation for students to pursue further studies of advanced quantum mechanics and stresses the importance of translating quantum insights into useful and tangible innovations and inventions. As such, this is the only work to cover semiconductor nanotechnology from the perspective of introductory quantum mechanics, with applications including mainstream semiconductor technologies as well as (nano)devices, ranging from photodetectors, laser diodes, and solar cells to transistors and Schottky contacts. Problems are also provided to test the reader's understanding and supplementary material available includes working presentation files, solutions and instructors manuals. (orig.)

  2. Quantum mechanics and electrodynamics

    CERN Document Server

    Zamastil, Jaroslav

    2017-01-01

    This book highlights the power and elegance of algebraic methods of solving problems in quantum mechanics. It shows that symmetries not only provide elegant solutions to problems that can be solved exactly, but also substantially simplify problems that must be solved approximately. Furthermore, the book provides an elementary exposition of quantum electrodynamics and its application to low-energy physics, along with a thorough analysis of the role of relativistic, magnetic, and quantum electrodynamic effects in atomic spectroscopy. Included are essential derivations made clear through detailed, transparent calculations. The book’s commitment to deriving advanced results with elementary techniques, as well as its inclusion of exercises will enamor it to advanced undergraduate and graduate students.

  3. Quantum mechanics and hidden superconformal symmetry

    Science.gov (United States)

    Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

    2017-12-01

    Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).

  4. Quantum Mechanics with a Little Less Mystery

    Science.gov (United States)

    Cropper, William H.

    1969-01-01

    Suggests the "route of the inquiring mind in presenting the esoteric quantum mechanical postulates and concepts in an understandable form. Explains that the quantum mechanical postulates are but useful mathematical forms to express thebroader principles of superposition and correspondence. Briefly describes some of the features which makes the…

  5. Grid-Based Projector Augmented Wave (GPAW) Implementation of Quantum Mechanics/Molecular Mechanics (QM/MM) Electrostatic Embedding and Application to a Solvated Diplatinum Complex

    DEFF Research Database (Denmark)

    Dohn, A. O.; Jónsson, E. Ö.; Levi, Gianluca

    2017-01-01

    A multiscale density functional theory-quantum mechanics/molecular mechanics (DFT-QM/MM) scheme is presented, based on an efficient electrostatic coupling between the electronic density obtained from a grid-based projector augmented wave (GPAW) implementation of density functional theory...... and a classical potential energy function. The scheme is implemented in a general fashion and can be used with various choices for the descriptions of the QM or MM regions. Tests on H2O clusters, ranging from dimer to decamer show that no systematic energy errors are introduced by the coupling that exceeds...

  6. On phase-space representations of quantum mechanics using

    Indian Academy of Sciences (India)

    space representations of quantum mechanics using Glauber coherent states. DIÓGENES CAMPOS. Research Article Volume 87 Issue 2 August ... Keywords. Phase-space quantum mechanics, coherent states, Husimi function, Wigner function ...

  7. The conceptual foundations of quantum mechanics

    CERN Document Server

    Eisenbud, Leonard

    2007-01-01

    This book provides a clear and logical path to understanding what quantum mechanics is about. It will be accessible to undergraduates with minimal mathematical preparation: all that is required is an open mind, a little algebra, and a first course in undergraduate physics. Quantum mechanics is arguably the most successful physical theory. It makes predictions of incredible accuracy. It provides the structure underlying all of our electronic technology, and much of our mastery over materials. But compared with Newtonian mechanics, or even relativity, its teachings seem obscure-they have no coun

  8. Quantum mechanics as applied mathematical statistics

    International Nuclear Information System (INIS)

    Skala, L.; Cizek, J.; Kapsa, V.

    2011-01-01

    Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.

  9. Beyond conventional quantum mechanics

    International Nuclear Information System (INIS)

    Ghirardi, C.

    1991-10-01

    The author reviews some recent attempts to overcome the conceptual difficulties encountered by trying to interpret quantum mechanics as giving a complete, objective and unified description of natural phenomena. 38 refs

  10. Supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Crombrugghe, M. de; Rittenberg, V.

    1982-12-01

    We give a general construction for supersymmetric Hamiltonians in quantum mechanics. We find that N-extended supersymmetry imposes very strong constraints, and for N > 4 the Hamiltonian is integrable. We give a variety of examples, for one-particle and for many-particle systems, in different numbers of dimensions. (orig.)

  11. Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction.

    Science.gov (United States)

    Budiyono, Agung; Rohrlich, Daniel

    2017-11-03

    Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic framework, allowing an unambiguous account of how one theory is the limit of the other. Here we derive non-relativistic quantum mechanics and classical statistical mechanics within a common framework. The common axioms include conservation of average energy and conservation of probability current. But two axioms distinguish quantum mechanics from classical statistical mechanics: an "ontic extension" defines a nonseparable (global) random variable that generates physical correlations, and an "epistemic restriction" constrains allowed phase space distributions. The ontic extension and epistemic restriction, with strength on the order of Planck's constant, imply quantum entanglement and uncertainty relations. This framework suggests that the wave function is epistemic, yet it does not provide an ontic dynamics for individual systems.

  12. Third-order differential ladder operators and supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Mateo, J; Negro, J

    2008-01-01

    Hierarchies of one-dimensional Hamiltonians in quantum mechanics admitting third-order differential ladder operators are studied. Each Hamiltonian has associated three-step Darboux (pseudo)-cycles and Painleve IV equations as a closure condition. The whole hierarchy is generated applying some operations on the cycles. These operations are investigated in the frame of supersymmetric quantum mechanics and mainly involve algebraic manipulations. A consistent geometric representation for the hierarchy and cycles is built that also helps in understanding the operations. Three kinds of hierarchies are distinguished and a realization based on the harmonic oscillator Hamiltonian is supplied, giving an interpretation for the spectral properties of the Hamiltonians of each hierarchy

  13. Ultrafast quantum random number generation based on quantum phase fluctuations.

    Science.gov (United States)

    Xu, Feihu; Qi, Bing; Ma, Xiongfeng; Xu, He; Zheng, Haoxuan; Lo, Hoi-Kwong

    2012-05-21

    A quantum random number generator (QRNG) can generate true randomness by exploiting the fundamental indeterminism of quantum mechanics. Most approaches to QRNG employ single-photon detection technologies and are limited in speed. Here, we experimentally demonstrate an ultrafast QRNG at a rate over 6 Gbits/s based on the quantum phase fluctuations of a laser operating near threshold. Moreover, we consider a potential adversary who has partial knowledge on the raw data and discuss how one can rigorously remove such partial knowledge with postprocessing. We quantify the quantum randomness through min-entropy by modeling our system and employ two randomness extractors--Trevisan's extractor and Toeplitz-hashing--to distill the randomness, which is information-theoretically provable. The simplicity and high-speed of our experimental setup show the feasibility of a robust, low-cost, high-speed QRNG.

  14. Quantum mechanical suppression of chaos

    International Nuclear Information System (INIS)

    Bluemel, R.; Smilansky, U.

    1990-01-01

    The relation between determinism and predictability is the central issue in the study of 'deterministic chaos'. Much knowledge has been accumulated in the past 10 years about the chaotic dynamics of macroscopic (classical) systems. The implications of chaos in the microscopic quantum world is examined, in other words, how to reconcile the correspondence principle with the inherent uncertainties which reflect the wave nature of quantum dynamics. Recent atomic physics experiments demonstrate clearly that chaos is relevant to the microscopic world. In particular, such experiments emphasise the urgent need to clarify the genuine quantum mechanism which imposes severe limitations on quantum dynamics, and renders it so very different from its classical counterpart. (author)

  15. Linear-scaling quantum mechanical methods for excited states.

    Science.gov (United States)

    Yam, ChiYung; Zhang, Qing; Wang, Fan; Chen, GuanHua

    2012-05-21

    The poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and

  16. Dynamics in the quantum/classical limit based on selective use of the quantum potential

    International Nuclear Information System (INIS)

    Garashchuk, Sophya; Dell’Angelo, David; Rassolov, Vitaly A.

    2014-01-01

    A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction

  17. Dynamics in the quantum/classical limit based on selective use of the quantum potential

    Energy Technology Data Exchange (ETDEWEB)

    Garashchuk, Sophya, E-mail: garashchuk@sc.edu; Dell’Angelo, David; Rassolov, Vitaly A. [Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208 (United States)

    2014-12-21

    A classical limit of quantum dynamics can be defined by compensation of the quantum potential in the time-dependent Schrödinger equation. The quantum potential is a non-local quantity, defined in the trajectory-based form of the Schrödinger equation, due to Madelung, de Broglie, and Bohm, which formally generates the quantum-mechanical features in dynamics. Selective inclusion of the quantum potential for the degrees of freedom deemed “quantum,” defines a hybrid quantum/classical dynamics, appropriate for molecular systems comprised of light and heavy nuclei. The wavefunction is associated with all of the nuclei, and the Ehrenfest, or mean-field, averaging of the force acting on the classical degrees of freedom, typical of the mixed quantum/classical methods, is avoided. The hybrid approach is used to examine evolution of light/heavy systems in the harmonic and double-well potentials, using conventional grid-based and approximate quantum-trajectory time propagation. The approximate quantum force is defined on spatial domains, which removes unphysical coupling of the wavefunction fragments corresponding to distinct classical channels or configurations. The quantum potential, associated with the quantum particle, generates forces acting on both quantum and classical particles to describe the backreaction.

  18. Supersymmetry in quantum mechanics

    International Nuclear Information System (INIS)

    Lahiri, A.; Roy, P.K.; Bagghi, B.

    1990-01-01

    A pedagogical review on supersymmetry in quantum mechanics is presented which provides a comprehensive coverage of the subject. First, the key ingredients of the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltonian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. The authors also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N = 1 and N = 2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. They treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called 'shape-invariance' of potentials. To make transparent the relationship between supersymmetry and solvable potentials, they also solve several examples. They then go over the formulation of supersymmetry in radial problems, paying a special attention to the Coulomb and isotropic oscillator potentials. They show that the ladder operator technique may be suitable modified in higher dimensions for generating isospectral Hamiltonians. Next, the criteria for the breaking of supersymmetry is considered and their range of applicability is examined by suitably modifying he definition of Witten's index. Finally, the authors perform some numerical calculations for a class of potentials to show how a modified WKB approximation works in supersymmetric cases

  19. The interpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Pippard, A.B.

    1986-01-01

    It is argued that the reduction of the wavepacket following a measurement is no more than a computational convenience to which no meaning should be attached. In a strict application of quantum mechanics all measuring instruments must be included in a single wavefunction. Thus the activity of physics is treated as the analysis of public information, as conveyed by instruments, with quantum mechanics the accepted analytical procedure rather than a model of objective reality. Finally the classical world of particle trajectories that can be agreed on by all observers is shown to be a natural corollary. (author)

  20. Quantum mechanics reality and separability

    International Nuclear Information System (INIS)

    Selleri, F.; Tarozzi, G.

    1981-01-01

    For many decades, there has been a debate about which one should be the correct interpretation of Quantum Mechanics. With regard to this question, the Copenhagen-Goettingen interpretation was in conflict with the interpretation given by Einstein and other physicists. The so-called problem of ''completeness'' of the theory in particular was under investigation. The development of this controversial problem, from the Von Neumann theorem up to the discovery of Bell inequality is reviewed in this article and it is discussed how these events marked the beginning of a new era for the researches on Quantum Mechanics. (author)

  1. Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and Thermodynamics

    OpenAIRE

    Beretta, Gian Paolo

    2006-01-01

    We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy stat...

  2. Fragment-based quantum mechanical calculation of protein-protein binding affinities.

    Science.gov (United States)

    Wang, Yaqian; Liu, Jinfeng; Li, Jinjin; He, Xiao

    2018-04-29

    The electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method has been successfully utilized for efficient linear-scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE-GMFCC method for calculation of binding affinity of Endonuclease colicin-immunity protein complex. The binding free energy changes between the wild-type and mutants of the complex calculated by EE-GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6-31G*-D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein-protein binding affinities. Moreover, the self-consistent calculation of PB solvation energy is required for accurate calculations of protein-protein binding free energies. This study demonstrates that the EE-GMFCC method is capable of providing reliable prediction of relative binding affinities for protein-protein complexes. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

  3. Limits to the universality of quantum mechanics

    International Nuclear Information System (INIS)

    Josephson, B.D.

    1988-01-01

    Niels Bohr's arguments indicating the non-applicability of quantum methodology to the study of the ultimate details of life, given in his book Atomic Physics and Human Knowledge, conflict with the commonly held opposite view. The bases for the usual beliefs are examined and shown to have little validity; significant differences do exist between the living organism and the type of system studied successfully in the physics laboratory. Dealing with living organisms in quantum-mechanical terms with the same degree of rigor as is normal for non-living systems would seem not to be possible without considering also questions of the origins of life and of the universe

  4. Quantum mechanics in simple matrix form

    CERN Document Server

    Jordan, Thomas F

    1986-01-01

    With this text, basic quantum mechanics becomes accessible to undergraduates with no background in mathematics beyond algebra. Containing more than 100 problems, it provides an easy way to learn part of the quantum language and to employ this new skill in solving problems.

  5. On quantum chaos, stochastic webs and localization in a quantum mechanical kick system

    International Nuclear Information System (INIS)

    Engel, U.M.

    2007-01-01

    In this study quantum chaos is discussed using the kicked harmonic oscillator as a model system. The kicked harmonic oscillator is characterized by an exceptional scenario of weak chaos: In the case of resonance between the frequency of the harmonic oscillator and the frequency of the periodic forcing, stochastic webs in phase space are generated by the classical dynamics. For the quantum dynamics of this system it is shown that the resulting Husimi distributions in quantum phase space exhibit the same web-like structures as the classical webs. The quantum dynamics is characterized by diffusive energy growth - just as the classical dynamics in the channels of the webs. In the case of nonresonance, the classically diffusive dynamics is found to be quantum mechanically suppressed. This bounded energy growth, which corresponds to localization in quantum phase space, is explained analytically by mapping the system onto the Anderson model. In this way, within the context of quantum chaos, the kicked harmonic oscillator is characterized by exhibiting its noteworthy geometrical and dynamical properties both classically and quantum mechanically, while at the same time there are also very distinct quantum deviations from classical properties, the most prominent example being quantum localization. (orig.)

  6. Holistic aspects of quantum mechanics

    International Nuclear Information System (INIS)

    Pietschmann, H.

    1987-01-01

    Aspects of quantum mechanics irreconcilable with classical physics are outlined. Quantum mechanics started with a negative statement about reality, namely: it is impossible to determine momentum and position of a particle simultaneously. Meanwhile it has generated an impressive body of predictions which can be tested and have been confirmed by suitable experiments. As a consequence a naive, local, materialistic concept of reality must be abolished and a novel approach, the holistic is introduced. This is illustrated by some examples e.g. the Pauli exclusion principle for electrons, the electron capture decay of 135 La as a model of the wavefunction reduction, the Bohr radius of the atom, electron localisation in the atom. An example from the quantum field theory is the calculation of magnetic moments of electron and muon where a particle cannot be considered separately and all other particles must be taken into account. (G.Q.)

  7. Speakable and unspeakable in quantum mechanics. 2. corr. ed.

    International Nuclear Information System (INIS)

    Bell, John S.

    2015-01-01

    The new, completely revised translation of the English original edition ''Speakable and Unspeakable in quantum mechanics'' contains both all published and unpublished articles of John Bell about the conceptional and philosophical problems of quantum mechanics as for instance ''About the Einstein-Podolsky-Rosen paradoxon'', ''Bertlmann's Socks and the ''Essence of Reality'', or ''Six Possible Worlds of Quantum Mechanics''. For our presnet understanding of quantum concepts and their limited applicability to classical conceptions of space, time, and locality his works have played an eminent role. After a short foreword of John Bell Alain Aspect explains the huge contribution, which John Bell has provided in Quantum philosophy.

  8. Introduction to nonequilibrium statistical mechanics with quantum field theory

    International Nuclear Information System (INIS)

    Kita, Takafumi

    2010-01-01

    In this article, we present a concise and self-contained introduction to nonequilibrium statistical mechanics with quantum field theory by considering an ensemble of interacting identical bosons or fermions as an example. Readers are assumed to be familiar with the Matsubara formalism of equilibrium statistical mechanics such as Feynman diagrams, the proper self-energy, and Dyson's equation. The aims are threefold: (1) to explain the fundamentals of nonequilibrium quantum field theory as simple as possible on the basis of the knowledge of the equilibrium counterpart; (2) to elucidate the hierarchy in describing nonequilibrium systems from Dyson's equation on the Keldysh contour to the Navier-Stokes equation in fluid mechanics via quantum transport equations and the Boltzmann equation; (3) to derive an expression of nonequilibrium entropy that evolves with time. In stage (1), we introduce nonequilibrium Green's function and the self-energy uniquely on the round-trip Keldysh contour, thereby avoiding possible confusions that may arise from defining multiple Green's functions at the very beginning. We try to present the Feynman rules for the perturbation expansion as simple as possible. In particular, we focus on the self-consistent perturbation expansion with the Luttinger-Ward thermodynamic functional, i.e., Baym's Φ-derivable approximation, which has a crucial property for nonequilibrium systems of obeying various conservation laws automatically. We also show how the two-particle correlations can be calculated within the Φ-derivable approximation, i.e., an issue of how to handle the 'Bogoliubov-Born-Green-Kirkwood-Yvons (BBGKY) hierarchy'. Aim (2) is performed through successive reductions of relevant variables with the Wigner transformation, the gradient expansion based on the Groenewold-Moyal product, and Enskog's expansion from local equilibrium. This part may be helpful for convincing readers that nonequilibrium systems can be handled microscopically with

  9. Completing Quantum Mechanics with Quantized Hidden Variables

    OpenAIRE

    van Enk, S. J.

    2015-01-01

    I explore the possibility that a quantum system S may be described completely by the combination of its standard quantum state $|\\psi\\rangle$ and a (hidden) quantum state $|\\phi\\rangle$ (that lives in the same Hilbert space), such that the outcome of any standard projective measurement on the system S is determined once the two quantum states are specified. I construct an algorithm that retrieves the standard quantum-mechanical probabilities, which depend only on $|\\psi\\rangle$, by assuming t...

  10. Exponential complexity and ontological theories of quantum mechanics

    International Nuclear Information System (INIS)

    Montina, A.

    2008-01-01

    Ontological theories of quantum mechanics describe a single system by means of well-defined classical variables and attribute the quantum uncertainties to our ignorance about the underlying reality represented by these variables. We consider the general class of ontological theories describing a quantum system by a set of variables with Markovian (either deterministic or stochastic) evolution. We provide proof that the number of continuous variables cannot be smaller than 2N-2, N being the Hilbert-space dimension. Thus, any ontological Markovian theory of quantum mechanics requires a number of variables which grows exponentially with the physical size. This result is relevant also in the framework of quantum Monte Carlo methods

  11. Quantum mechanics.Text and exercise book. 2. upd. ed.

    International Nuclear Information System (INIS)

    Griffiths, David J.

    2012-01-01

    The modern life would be without quantum mechanics no more imaginable - on their laws are founded transistors, computer chips, mobile telephones, flat displays, and numerous other things of daily life. An understanding of this theory is indispensable in order to be able to settle a matter with questions of temporary physics. Griffith's ''Intorduction to Quantum Mechanics'' presents the fundamental laws of quantum mechanics, puts carefully the mathematical foundations of the theory, and presents essential applications of quantum mechanics from the hydrogen atom until Schroedinger's cat. This book applies to studyings of natural sciences, especially of physics. It is concipated for studyings of bachelor courses at universities and throws a bridge between the conceptual core of quantum mechanics and the mathematically often expensive application to real problems. For this numerous problems are completely worked out in order to fill the matter with life. Rounded off are all chapters by a manifold of problems of all degrees of difficulty, which allow the studyings to deepen their knowledge and apply immediately. Beside a course accompanying the ''Introduction to Quantum Mechanics'' is therefore also suited for the self-study.

  12. Experimental status of quaternionic quantum mechanics

    International Nuclear Information System (INIS)

    Brumby, S.P.; Joshi, G.C.

    1995-01-01

    Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. The only direct search for quaternionic quantum mechanics yet carried out is reviewed and is proposed to look for quaternionic effects in correlated multi-particle systems. It is also discussed how such experiments might distinguish between the several quaternionic models proposed in the literature. 21 refs

  13. Introductory quantum mechanics for applied nanotechnology

    CERN Document Server

    Kim, Dae Mann

    2015-01-01

    This introductory textbook covers fundamental quantum mechanics from an application perspective, considering optoelectronic devices, biological sensors and molecular imagers as well as solar cells and field effect transistors. The book provides a brief review of classical and statistical mechanics and electromagnetism, and then turns to the quantum treatment of atoms, molecules, and chemical bonds. Aiming at senior undergraduate and graduate students in nanotechnology related areas like physics, materials science, and engineering, the book could be used at schools that offer interdisciplinary but focused training for future workers in the semiconductor industry and for the increasing number of related nanotechnology firms, and even practicing people could use it when they need to learn related concepts. The author is Professor Dae Mann Kim from the Korea Institute for Advanced Study who has been teaching Quantum Mechanics to engineering, material science and physics students for over 25 years in USA and Asia.

  14. A mathematical primer on quantum mechanics

    CERN Document Server

    Teta, Alessandro

    2018-01-01

    This book offers a rigorous yet elementary approach to quantum mechanics that will meet the needs of Master’s-level Mathematics students and is equally suitable for Physics students who are interested in gaining a deeper understanding of the mathematical structure of the theory. Throughout the coverage, which is limited to single-particle quantum mechanics, the focus is on formulating theory and developing applications in a mathematically precise manner. Following a review of selected key concepts in classical physics and the historical background, the basic elements of the theory of operators in Hilbert spaces are presented and used to formulate the rules of quantum mechanics. The discussion then turns to free particles, harmonic oscillators, delta potential, and hydrogen atoms, providing rigorous proofs of the corresponding dynamical properties. Starting from an analysis of these applications, readers are subsequently introduced to more advanced topics such as the classical limit, scattering theory, and s...

  15. Horizon quantum mechanics of rotating black holes

    Energy Technology Data Exchange (ETDEWEB)

    Casadio, Roberto [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Giugno, Andrea [Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Giusti, Andrea [Universita di Bologna, Dipartimento di Fisica e Astronomia, Bologna (Italy); I.N.F.N., Sezione di Bologna, I.S. FLAG, Bologna (Italy); Ludwig-Maximilians-Universitaet, Arnold Sommerfeld Center, Munich (Germany); Micu, Octavian [Institute of Space Science, Bucharest, P.O. Box MG-23, Bucharest-Magurele (Romania)

    2017-05-15

    The horizon quantum mechanics is an approach that was previously introduced in order to analyze the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. In this work, we first extend the formalism to general space-times with asymptotic (ADM) mass and angular momentum. We then apply the extended horizon quantum mechanics to a harmonic model of rotating corpuscular black holes. We find that simple configurations of this model naturally suppress the appearance of the inner horizon and seem to disfavor extremal (macroscopic) geometries. (orig.)

  16. Superconducting Qubits as Mechanical Quantum Engines.

    Science.gov (United States)

    Sachtleben, Kewin; Mazon, Kahio T; Rego, Luis G C

    2017-09-01

    We propose the equivalence of superconducting qubits with a pistonlike mechanical quantum engine. The work reports a study on the nature of the nonequilibrium work exchanged with the quantum-nonadiabatic working medium, which is modeled as a multilevel coupled quantum well system subject to an external control parameter. The quantum dynamics is solved for arbitrary control protocols. It is shown that the work output has two components: one that depends instantaneously on the level populations and another that is due to the quantum coherences built in the system. The nonadiabatic coherent dynamics of the quantum engine gives rise to a resistance (friction) force that decreases the work output. We consider the functional equivalence of such a device and a rf-SQUID flux qubit.

  17. Euler and applications of quantum mechanics. Paradox IH. Part 1

    Directory of Open Access Journals (Sweden)

    IVASYSHIN Henrich Stepanovich

    2014-04-01

    Full Text Available By some estimation, thirty percent of the gross national product of the USA depends on the applications of quantum mechanics in one or another form. Different aspects of the development of quantum theory are considered. Based on the residual stresses and relaxation of the stresses in the details of arbitrary forms the analysis of technological option of the Einstein–Podolsky–Rosen paradox interpretation is performed by the method of shaped coordination grid. The option refers to the mystery of measurement of two particles which are located far from each other but at the same time which quantum states are interconnected. The paper also regards the application of involute with variable evolute to increase working capacity of interfaces in free wheels, gearing and ribbon and rack mechanisms.

  18. Density functional theory and quantum mechanics/molecular mechanics study of cysteine protease inhibition by nitrile-based inhibitors.

    Directory of Open Access Journals (Sweden)

    Sam P De Visser

    2013-12-01

    Full Text Available Cysteine protease enzymes are important for human physiology and catalyze key protein degradation pathways. These enzymes react via a nucleophilic reaction mechanism that involves a cysteine residue and the proton of a proximal histidine. Particularly efficient inhibitors of these enzymes are nitrile-based, however, the details of the catalytic reaction mechanism currently are poorly understood. To gain further insight into the inhibition of these molecules, we have performed a combined density functional theory and quantum mechanics/molecular mechanics study on the reaction of a nitrile-based inhibitor with the enzyme active site amino acids. We show here that small perturbations to the inhibitor structure can have dramatic effects on the catalysis and inhibition processes. Thus, we investigated a range of inhibitor templates and show that specific structural changes reduce the inhibitory efficiency by several orders of magnitude. Moreover, as the reaction takes place on a polar surface, we find strong differences between the DFT and QM/MM calculated energetics. In particular, the DFT model led to dramatic distortions from the starting structure and the convergence to a structure that would not fit the enzyme active site. In the subsequent QM/MM study we investigated the use of mechanical versus electronic embedding on the kinetics, thermodynamics and geometries along the reaction mechanism. We find minor effects on the kinetics of the reaction but large geometric and thermodynamics differences as a result of inclusion of electronic embedding corrections. The work here highlights the importance of model choice in the investigation of this biochemical reaction mechanism.

  19. Statistics, synergy, and mechanism of multiple photogeneration of excitons in quantum dots: Fundamental and applied aspects

    International Nuclear Information System (INIS)

    Oksengendler, B. L.; Turaeva, N. N.; Uralov, I.; Marasulov, M. B.

    2012-01-01

    The effect of multiple exciton generation is analyzed based on statistical physics, quantum mechanics, and synergetics. Statistical problems of the effect of multiple exciton generation (MEG) are broadened and take into account not only exciton generation, but also background excitation. The study of the role of surface states of quantum dots is based on the synergy of self-catalyzed electronic reactions. An analysis of the MEG mechanism is based on the idea of electronic shaking using the sudden perturbation method in quantum mechanics. All of the above-mentioned results are applied to the problem of calculating the limiting efficiency to transform solar energy into electric energy. (authors)

  20. Path Integrals in Quantum Mechanics

    International Nuclear Information System (INIS)

    Louko, J

    2005-01-01

    Jean Zinn-Justin's textbook Path Integrals in Quantum Mechanics aims to familiarize the reader with the path integral as a calculational tool in quantum mechanics and field theory. The emphasis is on quantum statistical mechanics, starting with the partition function Tr exp(-β H) and proceeding through the diffusion equation to barrier penetration problems and their semiclassical limit. The 'real time' path integral is defined via analytic continuation and used for the path-integral representation of the nonrelativistic S-matrix and its perturbative expansion. Holomorphic and Grassmannian path integrals are introduced and applied to nonrelativistic quantum field theory. There is also a brief discussion of path integrals in phase space. The introduction includes a brief historical review of path integrals, supported by a bibliography with some 40 entries. As emphasized in the introduction, mathematical rigour is not a central issue in the book. This allows the text to present the calculational techniques in a very readable manner: much of the text consists of worked-out examples, such as the quartic anharmonic oscillator in the barrier penetration chapter. At the end of each chapter there are exercises, some of which are of elementary coursework type, but the majority are more in the style of extended examples. Most of the exercises indeed include the solution or a sketch thereof. The book assumes minimal previous knowledge of quantum mechanics, and some basic quantum mechanical notation is collected in an appendix. The material has a large overlap with selected chapters in the author's thousand-page textbook Quantum Field Theory and Critical Phenomena (2002 Oxford: Clarendon). The stand-alone scope of the present work has, however, allowed a more focussed organization of this material, especially in the chapters on, respectively, holomorphic and Grassmannian path integrals. In my view the book accomplishes its aim admirably and is eminently usable as a textbook

  1. Quantum causality conceptual issues in the causal theory of quantum mechanics

    CERN Document Server

    Riggs, Peter J; French, Steven RD

    2009-01-01

    This is a treatise devoted to the foundations of quantum physics and the role that causality plays in the microscopic world governed by the laws of quantum mechanics. The book is controversial and will engender some lively debate on the various issues raised.

  2. Quantum mechanics. Mechanically detecting and avoiding the quantum fluctuations of a microwave field.

    Science.gov (United States)

    Suh, J; Weinstein, A J; Lei, C U; Wollman, E E; Steinke, S K; Meystre, P; Clerk, A A; Schwab, K C

    2014-06-13

    Quantum fluctuations of the light field used for continuous position detection produce stochastic back-action forces and ultimately limit the sensitivity. To overcome this limit, the back-action forces can be avoided by giving up complete knowledge of the motion, and these types of measurements are called "back-action evading" or "quantum nondemolition" detection. We present continuous two-tone back-action evading measurements with a superconducting electromechanical device, realizing three long-standing goals: detection of back-action forces due to the quantum noise of a microwave field, reduction of this quantum back-action noise by 8.5 ± 0.4 decibels (dB), and measurement imprecision of a single quadrature of motion 2.4 ± 0.7 dB below the mechanical zero-point fluctuations. Measurements of this type will find utility in ultrasensitive measurements of weak forces and nonclassical states of motion. Copyright © 2014, American Association for the Advancement of Science.

  3. The role of the rigged Hilbert space in quantum mechanics

    International Nuclear Information System (INIS)

    Madrid, Rafael de la

    2005-01-01

    There is compelling evidence that, when a continuous spectrum is present, the natural mathematical setting for quantum mechanics is the rigged Hilbert space rather than just the Hilbert space. In particular, Dirac's braket formalism is fully implemented by the rigged Hilbert space rather than just by the Hilbert space. In this paper, we provide a pedestrian introduction to the role the rigged Hilbert space plays in quantum mechanics, by way of a simple, exactly solvable example. The procedure will be constructive and based on a recent publication. We also provide a thorough discussion on the physical significance of the rigged Hilbert space

  4. Relativistic quantum mechanics an introduction to relativistic quantum fields

    CERN Document Server

    Maiani, Luciano

    2016-01-01

    Written by two of the world's leading experts on particle physics and the standard model - including an award-winning former Director General of CERN - this textbook provides a completely up-to-date account of relativistic quantum mechanics and quantum field theory. It describes the formal and phenomenological aspects of the standard model of particle physics, and is suitable for advanced undergraduate and graduate students studying both theoretical and experimental physics.

  5. Calculating the C operator in PT-symmetric quantum mechanics

    International Nuclear Information System (INIS)

    Bender, C.M.

    2004-01-01

    It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT-symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition it is cumbersome to calculate C in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method can be used to calculate the C operator in quantum field theory. The C operator is a new time-independent observable in PT-symmetric quantum field theory. (author)

  6. Predicted phototoxicities of carbon nano-material by quantum mechanical calculations

    Science.gov (United States)

    The purpose of this research is to develop a predictive model for the phototoxicity potential of carbon nanomaterials (fullerenols and single-walled carbon nanotubes). This model is based on the quantum mechanical (ab initio) calculations on these carbon-based materials and compa...

  7. Externally predictive quantitative modeling of supercooled liquid vapor pressure of polychlorinated-naphthalenes through electron-correlation based quantum-mechanical descriptors.

    Science.gov (United States)

    Vikas; Chayawan

    2014-01-01

    For predicting physico-chemical properties related to environmental fate of molecules, quantitative structure-property relationships (QSPRs) are valuable tools in environmental chemistry. For developing a QSPR, molecular descriptors computed through quantum-mechanical methods are generally employed. The accuracy of a quantum-mechanical method, however, rests on the amount of electron-correlation estimated by the method. In this work, single-descriptor QSPRs for supercooled liquid vapor pressure of chloronaphthalenes and polychlorinated-naphthalenes are developed using molecular descriptors based on the electron-correlation contribution of the quantum-mechanical descriptor. The quantum-mechanical descriptors for which the electron-correlation contribution is analyzed include total-energy, mean polarizability, dipole moment, frontier orbital (HOMO/LUMO) energy, and density-functional theory (DFT) based descriptors, namely, absolute electronegativity, chemical hardness, and electrophilicity index. A total of 40 single-descriptor QSPRs were developed using molecular descriptors computed with advanced semi-empirical (SE) methods, namely, RM1, PM7, and ab intio methods, namely, Hartree-Fock and DFT. The developed QSPRs are validated using state-of-the-art external validation procedures employing an external prediction set. From the comparison of external predictivity of the models, it is observed that the single-descriptor QSPRs developed using total energy and correlation energy are found to be far more robust and predictive than those developed using commonly employed descriptors such as HOMO/LUMO energy and dipole moment. The work proposes that if real external predictivity of a QSPR model is desired to be explored, particularly, in terms of intra-molecular interactions, correlation-energy serves as a more appropriate descriptor than the polarizability. However, for developing QSPRs, computationally inexpensive advanced SE methods such as PM7 can be more reliable than

  8. The ZX-calculus is complete for stabilizer quantum mechanics

    International Nuclear Information System (INIS)

    Backens, Miriam

    2014-01-01

    The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations. (paper)

  9. Tampering detection system using quantum-mechanical systems

    Science.gov (United States)

    Humble, Travis S [Knoxville, TN; Bennink, Ryan S [Knoxville, TN; Grice, Warren P [Oak Ridge, TN

    2011-12-13

    The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.

  10. Interactive Quantum Mechanics Quantum Experiments on the Computer

    CERN Document Server

    Brandt, S; Dahmen, H.D

    2011-01-01

    Extra Materials available on extras.springer.com INTERACTIVE QUANTUM MECHANICS allows students to perform their own quantum-physics experiments on their computer, in vivid 3D color graphics. Topics covered include: •        harmonic waves and wave packets, •        free particles as well as bound states and scattering in various potentials in one and three dimensions (both stationary and time dependent), •        two-particle systems, coupled harmonic oscillators, •        distinguishable and indistinguishable particles, •        coherent and squeezed states in time-dependent motion, •        quantized angular momentum, •        spin and magnetic resonance, •        hybridization. For the present edition the physics scope has been widened appreciably. Moreover, INTERQUANTA can now produce user-defined movies of quantum-mechanical situations. Movies can be viewed directly and also be saved to be shown later in any browser. Sections on spec...

  11. Entangled states in quantum mechanics

    Science.gov (United States)

    Ruža, Jānis

    2010-01-01

    In some circles of quantum physicists, a view is maintained that the nonseparability of quantum systems-i.e., the entanglement-is a characteristic feature of quantum mechanics. According to this view, the entanglement plays a crucial role in the solution of quantum measurement problem, the origin of the “classicality” from the quantum physics, the explanation of the EPR paradox by a nonlocal character of the quantum world. Besides, the entanglement is regarded as a cornerstone of such modern disciplines as quantum computation, quantum cryptography, quantum information, etc. At the same time, entangled states are well known and widely used in various physics areas. In particular, this notion is widely used in nuclear, atomic, molecular, solid state physics, in scattering and decay theories as well as in other disciplines, where one has to deal with many-body quantum systems. One of the methods, how to construct the basis states of a composite many-body quantum system, is the so-called genealogical decomposition method. Genealogical decomposition allows one to construct recurrently by particle number the basis states of a composite quantum system from the basis states of its forming subsystems. These coupled states have a structure typical for entangled states. If a composite system is stable, the internal structure of its forming basis states does not manifest itself in measurements. However, if a composite system is unstable and decays onto its forming subsystems, then the measurables are the quantum numbers, associated with these subsystems. In such a case, the entangled state has a dynamical origin, determined by the Hamiltonian of the corresponding decay process. Possible correlations between the quantum numbers of resulting subsystems are determined by the symmetries-conservation laws of corresponding dynamical variables, and not by the quantum entanglement feature.

  12. What is Quantum Mechanics? A Minimal Formulation

    Science.gov (United States)

    Friedberg, R.; Hohenberg, P. C.

    2018-03-01

    This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen-Specker-Bell theorem and Gleason's theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.

  13. Double stochastic matrices in quantum mechanics

    International Nuclear Information System (INIS)

    Louck, J.D.

    1997-01-01

    The general set of doubly stochastic matrices of order n corresponding to ordinary nonrelativistic quantum mechanical transition probability matrices is given. Lande's discussion of the nonquantal origin of such matrices is noted. Several concrete examples are presented for elementary and composite angular momentum systems with the focus on the unitary symmetry associated with such systems in the spirit of the recent work of Bohr and Ulfbeck. Birkhoff's theorem on doubly stochastic matrices of order n is reformulated in a geometrical language suitable for application to the subset of quantum mechanical doubly stochastic matrices. Specifically, it is shown that the set of points on the unit sphere in cartesian n'-space is subjective with the set of doubly stochastic matrices of order n. The question is raised, but not answered, as to what is the subset of points of this unit sphere that correspond to the quantum mechanical transition probability matrices, and what is the symmetry group of this subset of matrices

  14. Quantum mechanics and the equivalence principle

    International Nuclear Information System (INIS)

    Davies, P C W

    2004-01-01

    A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurement is made far from the turning point of the classical trajectory. The results are then confirmed using the so-called dwell time definition of quantum tunnelling. I conclude with some remarks about the strong equivalence principle in quantum mechanics

  15. The influence of nonbilinear system-bath coupling on quantum-mechanical activated rate processes

    International Nuclear Information System (INIS)

    Navrotskaya, Irina; Geva, Eitan

    2006-01-01

    The dependence of quantum-mechanical activated rate processes on the system-bath coupling strength was investigated in the case of a double-well nonbilinearly coupled to a harmonic bath, where the system-bath coupling is linear in the bath coordinates and nonlinear in the reaction coordinate. Such nonbilinear coupling is known to give rise to a classical friction kernel which is explicitly dependent on the reaction coordinate. We show that it can also lead to quantum-mechanical barrier-crossing rates, whose dependence on the system-bath coupling strength is qualitatively different from that observed in the quantum-mechanical bilinear case and classical nonbilinear case. More specifically, it is shown that the quantum-mechanical barrier-crossing rate may monotonically increase as a function of the system-bath coupling strength, in cases where the classical barrier-crossing rate goes through a turnover, and that the rate of quantum-mechanical barrier-crossing can be lower than that of classical barrier-crossing. We show that those purely quantum-mechanical effects are of a thermodynamical, rather than dynamical, nature, and that they originate from the difference in friction between the barrier top and the reactant and product wells. Our conclusions are supported by results obtained via the CMD method, which were also found to be in very good agreement with numerically exact calculations based on the QUAPI method

  16. Tests of quantum mechanics and CPT symmetry with experimental data from CPLEAR

    CERN Document Server

    Miller, J P; Apostolakis, Alcibiades J; Aslanides, Elie; Backenstoss, Gerhard; Bargassa, P; Behnke, O; Benelli, A; Bertin, V; Blanc, F; Bloch, P; Carlson, P J; Carroll, M; Carvalho, J; Cawley, E; Chertok, M B; Danielsson, M; Dejardin, M; Derré, J; Ealet, A; Eleftheriadis, C; Faravel, L; Fetscher, W; Fidecaro, Maria; Filipcic, A; Francis, D; Fry, J; Gabathuler, Erwin; Gamet, R; Gerber, H J; Go, A; Haselden, A; Hayman, P J; Henry-Coüannier, F; Hollander, R W; Jon-And, K; Kettle, P R; Kokkas, P; Kreuger, R; Le Gac, R; Leimgruber, F; Mandic, I; Manthos, N; Marel, Gérard; Mikuz, M; Miller, J; Montanet, François; Müller, A; Nakada, Tatsuya; Pagels, B; Papadopoulos, I M; Pavlopoulos, P; Polivka, G; Rickenbach, R; Roberts, B L; Ruf, T; Schäfer, M; Schaller, L A; Schietinger, T; Schopper, A; Tauscher, Ludwig; Thibault, C; Touchard, F; Touramanis, C; van Eijk, C W E; Vlachos, S; Weber, P; Wigger, O; Wolter, M; Zavrtanik, D; Zimmerman, D; Ellis, Jonathan Richard; López, J L; Mavromatos, Nikolaos E; Nanopoulos, Dimitri V

    1999-01-01

    Data from the CPLEAR experiment are used to test CPT violation outside of regular quantum mechanics. The test is based on a model, motivated by Hawking's notion of loss of quantum coherence across a microscopic event horizon, which was developed in a particular version of string theory. (5 refs).

  17. A Bit of Quantum Mechanics

    Science.gov (United States)

    Oss, Stefano; Rosi, Tommaso

    2015-04-01

    We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called "common sense" based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.

  18. Optimal guidance law in quantum mechanics

    International Nuclear Information System (INIS)

    Yang, Ciann-Dong; Cheng, Lieh-Lieh

    2013-01-01

    Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction Ψ(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for Ψ(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function Ψ ∗ Ψ. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation

  19. Optimal guidance law in quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Ciann-Dong, E-mail: cdyang@mail.ncku.edu.tw; Cheng, Lieh-Lieh, E-mail: leo8101@hotmail.com

    2013-11-15

    Following de Broglie’s idea of a pilot wave, this paper treats quantum mechanics as a problem of stochastic optimal guidance law design. The guidance scenario considered in the quantum world is that an electron is the flight vehicle to be guided and its accompanying pilot wave is the guidance law to be designed so as to guide the electron to a random target driven by the Wiener process, while minimizing a cost-to-go function. After solving the stochastic optimal guidance problem by differential dynamic programming, we point out that the optimal pilot wave guiding the particle’s motion is just the wavefunction Ψ(t,x), a solution to the Schrödinger equation; meanwhile, the closed-loop guidance system forms a complex state–space dynamics for Ψ(t,x), from which quantum operators emerge naturally. Quantum trajectories under the action of the optimal guidance law are solved and their statistical distribution is shown to coincide with the prediction of the probability density function Ψ{sup ∗}Ψ. -- Highlights: •Treating quantum mechanics as a pursuit-evasion game. •Reveal an interesting analogy between guided flight motion and guided quantum motion. •Solve optimal quantum guidance problem by dynamic programming. •Gives a formal proof of de Broglie–Bohm’s idea of a pilot wave. •The optimal pilot wave is shown to be a wavefunction solved from Schrödinger equation.

  20. Quantum mechanics interpretation: scalled debate

    International Nuclear Information System (INIS)

    Sanchez Gomez, J. L.

    2000-01-01

    This paper discusses the two main issues of the so called quantum debate, that started in 1927 with the famous Bohr-Einstein controversy; namely non-separability and the projection postulate. Relevant interpretations and formulations of quantum mechanics are critically analyzed in the light of the said issues. The treatment is focused chiefly on fundamental points, so that technical ones are practically not dealt with here. (Author) 20 refs

  1. Tampering detection system using quantum-mechanical systems

    Energy Technology Data Exchange (ETDEWEB)

    Humble, Travis S [Knoxville, TN; Bennink, Ryan S [Knoxville, TN; Grice, Warren P [Oak Ridge, TN

    2011-12-13

    The use of quantum-mechanically entangled photons for monitoring the integrity of a physical border or a communication link is described. The no-cloning principle of quantum information science is used as protection against an intruder's ability to spoof a sensor receiver using a `classical` intercept-resend attack. Correlated measurement outcomes from polarization-entangled photons are used to protect against quantum intercept-resend attacks, i.e., attacks using quantum teleportation.

  2. On the Completeness of Quantum Mechanics

    OpenAIRE

    Kupczynski, Marian

    2002-01-01

    Quantum cryptography, quantum computer project, space-time quantization program and recent computer experiments reported by Accardi and his collaborators show the importance and actuality of the discussion of the completeness of quantum mechanics (QM) started by Einstein more than 70 years ago. Many years ago we pointed out that the violation of Bell's inequalities is neither a proof of completeness of QM nor an indication of the violation of Einsteinian causality. We also indicated how and i...

  3. Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields

    Science.gov (United States)

    Khrennikov, Andrei

    2017-02-01

    The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was a very special, although very important, example of

  4. Stochastic theories of quantum mechanics

    International Nuclear Information System (INIS)

    De la Pena, L.; Cetto, A.M.

    1991-01-01

    The material of this article is organized into five sections. In Sect. I the basic characteristics of quantum systems are briefly discussed, with emphasis on their stochastic properties. In Sect. II a version of stochastic quantum mechanics is presented, to conclude that the quantum formalism admits an interpretation in terms of stochastic processes. In Sect. III the elements of stochastic electrodynamics are described, and its possibilities and limitations as a fundamental theory of quantum systems are discussed. Section IV contains a recent reformulation that overcomes the limitations of the theory discussed in the foregoing section. Finally, in Sect. V the theorems of EPR, Von Neumann and Bell are discussed briefly. The material is pedagogically presented and includes an ample list of references, but the details of the derivations are generally omitted. (Author)

  5. Science Academies' Refresher Course in Quantum Mechanics Post ...

    Indian Academy of Sciences (India)

    Physics Dept

    2016-02-20

    Feb 20, 2016 ... Quantum Mechanics is essential for understanding Physics, Chemistry and even modern Biology. A brief outline of the course is as follows: Schrödinger equation, Hydrogen atom, mathematics of linear vector space, principles and postulates of quantum mechanics, angular momentum, perturbation theory.

  6. Essential quantum mechanics for electrotechnicians and informaticians; Essenzielle Quantenmechanik fuer Elektrotechniker und Informatiker

    Energy Technology Data Exchange (ETDEWEB)

    Deak, Peter [Bremen Univ. (Germany). Bremen Center for Computational Materials Science

    2016-07-01

    The motto of this book says ''quantum mechnaics in action''; the author demonstrated the surprising effects of quantum mechanics by means of direct applications, for instance in the illumination technology, in lasers, in photo- and solar cells, as well as in solid-state memories and quantum bits. The axioms and fundamental concepts of quantum mechanics are declared in the necessary, but as simple as possible mathematical formulation. Hereby only as much mathematica are used, as electrotechnicians and informaticians must learn apart from this. The necessary preliminary knowledges in mathematics and classical physics are besides summarized in appendices. Essential quantum mechanics for electrotechnicians and informaticians offers beyond foundations for continuing courses: The book comprehends the matter, which is important in connection with a course about classical physics and forms the base for the optional subject semiconductor physics in the master study. The additional material is multimedial: The numerous illustrations are supplemented by short video-clips and interactive simulations, applets visualize the results also graphically.

  7. Quasi-exactly solvable models in quantum mechanics

    International Nuclear Information System (INIS)

    Montemayor, R.; Salem, L.D.

    1990-01-01

    An extension of the application range of a method that studies partial resolution in quantum mechanics and that is based on the Ricatti equation, is carried out through adequately defined mappings. As an example of the use of these mappings, new families of Morse and Poeschl-Teller potentials are identified. A detailed discussion is made of their characteristics and the solutions obtained. (Author). 3 refs

  8. Quantum mechanics and the psyche

    Science.gov (United States)

    Galli Carminati, G.; Martin, F.

    2008-07-01

    In this paper we apply the last developments of the theory of measurement in quantum mechanics to the phenomenon of consciousness and especially to the awareness of unconscious components. Various models of measurement in quantum mechanics can be distinguished by the fact that there is, or there is not, a collapse of the wave function. The passive aspect of consciousness seems to agree better with models in which there is no collapse of the wave function, whereas in the active aspect of consciousness—i.e., that which goes together with an act or a choice—there seems to be a collapse of the wave function. As an example of the second possibility we study in detail the photon delayed-choice experiment and its consequences for subjective or psychological time. We apply this as an attempt to explain synchronicity phenomena. As a model of application of the awareness of unconscious components we study the mourning process. We apply also the quantum paradigm to the phenomenon of correlation at a distance between minds, as well as to group correlations that appear during group therapies or group training. Quantum entanglement leads to the formation of group unconscious or collective unconscious. Finally we propose to test the existence of such correlations during sessions of group training.

  9. Coherent Dynamics of a Hybrid Quantum Spin-Mechanical Oscillator System

    Science.gov (United States)

    Lee, Kenneth William, III

    A fully functional quantum computer must contain at least two important components: a quantum memory for storing and manipulating quantum information and a quantum data bus to securely transfer information between quantum memories. Typically, a quantum memory is composed of a matter system, such as an atom or an electron spin, due to their prolonged quantum coherence. Alternatively, a quantum data bus is typically composed of some propagating degree of freedom, such as a photon, which can retain quantum information over long distances. Therefore, a quantum computer will likely be a hybrid quantum device, consisting of two or more disparate quantum systems. However, there must be a reliable and controllable quantum interface between the memory and bus in order to faithfully interconvert quantum information. The current engineering challenge for quantum computers is scaling the device to large numbers of controllable quantum systems, which will ultimately depend on the choice of the quantum elements and interfaces utilized in the device. In this thesis, we present and characterize a hybrid quantum device comprised of single nitrogen-vacancy (NV) centers embedded in a high quality factor diamond mechanical oscillator. The electron spin of the NV center is a leading candidate for the realization of a quantum memory due to its exceptional quantum coherence times. On the other hand, mechanical oscillators are highly sensitive to a wide variety of external forces, and have the potential to serve as a long-range quantum bus between quantum systems of disparate energy scales. These two elements are interfaced through crystal strain generated by vibrations of the mechanical oscillator. Importantly, a strain interface allows for a scalable architecture, and furthermore, opens the door to integration into a larger quantum network through coupling to an optical interface. There are a few important engineering challenges associated with this device. First, there have been no

  10. Lectures on the mathematics of quantum mechanics I

    CERN Document Server

    Dell'Antonio, Gianfausto

    2015-01-01

    The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving th...

  11. Mindful Universe. Quantum mechanics and the participating observer

    International Nuclear Information System (INIS)

    Stapp, H.P.

    2007-01-01

    The classical mechanistic idea of nature that prevailed in science during the eighteenth and nineteenth centuries was an essentially mindless conception: the physically described aspects of nature were asserted to be completely determined by prior physically described aspects alone, with our conscious experiences entering only passively. During the twentieth century the classical concepts were found to be inadequate. In the new theory, quantum mechanics, our conscious experiences enter into the dynamics in specified ways not fixed by the physically described aspects alone. Consequences of this radical change in our understanding of the connection between mind and brain are described. ''Stapp's book is a bold and original attack on the problem of consciousness and free will based on the openings provided by the laws of quantum mechanics. This is a serious and interesting attack on a truly fundamental problem.'' (orig.)

  12. The birth of quantum mechanics

    International Nuclear Information System (INIS)

    Mehra, J.

    1976-01-01

    In an attempt to give an exact mathematical formulation of Bohr's Correspondence Principle, Heisenberg (June 1925) discovered the rules governing the behaviour of quantum- theoretical magnitudes. In fall 1925 Born, Heisenberg and Jordan and, independently, Dirac, formulated consistent algebraic schemes of quantum mechanics. Early in 1926 Schroedinger developed wave mechanics. In quick succession were discovered: Born's probability interpretation of the wave function, the transformation theory of Dirac, Jordan and F. London, Heisenberg's Uncertainty Relations and Bohr's Principle of Complementarity. By September 1927 the basis of a complete theory of atomic phenomena had been established. Aspects of this development, in which Heisenberg played a central role, are presented here as a tribute to his memory. (Author)

  13. Quantum-mechanical transport equation for atomic systems.

    Science.gov (United States)

    Berman, P. R.

    1972-01-01

    A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

  14. Quantum Information Biology: From Information Interpretation of Quantum Mechanics to Applications in Molecular Biology and Cognitive Psychology

    Science.gov (United States)

    Asano, Masanari; Basieva, Irina; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro

    2015-10-01

    We discuss foundational issues of quantum information biology (QIB)—one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from "traditional quantum biophysics". The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantum mechanics (its various forms were elaborated by Zeilinger and Brukner, Fuchs and Mermin, and D' Ariano) is the most natural interpretation of QIB. Biologically QIB is based on two principles: (a) adaptivity; (b) openness (bio-systems are fundamentally open). These principles are mathematically represented in the framework of a novel formalism— quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems.

  15. Problems in Quantum Mechanics with Solutions

    CERN Document Server

    d'Emilio, Emilio

    2011-01-01

    242 solved problems of several degrees of difficulty in nonrelativistic Quantum Mechanics, ranging from the themes of the crisis of classical physics, through the achievements in the framework of modern atomic physics, down to the still alive, more intriguing aspects connected e.g. with the EPR paradox, the Aharonov--Bohm effect, quantum teleportation.

  16. The reality problem in quantum mechanics

    International Nuclear Information System (INIS)

    Flamm, D.

    1988-01-01

    A series of 12 lectures on quantum mechanics and its inter-pretations: The more specific part begins with chapter 8: spin and polarization measurements; the Einstein-Podolski-Rosen paradoxon; Bell's inequations; interpretations of quantum theory; the role of the observer and the wave function of the world. 40 refs., 11 figs. (qui)

  17. A quantum mechanical model of "dark matter"

    OpenAIRE

    Belokurov, V. V.; Shavgulidze, E. T.

    2014-01-01

    The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.

  18. Do Free Quantum-Mechanical Wave Packets Always Spread?

    Science.gov (United States)

    Klein, James R.

    1980-01-01

    The spreading or shrinking of free three-dimensional quantum-mechanical wave packets is addressed. A seeming paradox concerning the time evolution operator and nonspreading wave packets is discussed, and the necessity of taking into account the appropriate mathematical structure of quantum mechanics is emphasized. Teaching implications are given.…

  19. The black hole S-Matrix from quantum mechanics

    NARCIS (Netherlands)

    Betzios, Panagiotis; Gaddam, Nava; Papadoulaki, Olga

    2016-01-01

    We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory \\& $c=1$ Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model\\textemdash of waves scattering off

  20. Optimization of metabolite detection by quantum mechanics simulations in magnetic resonance spectroscopy.

    Science.gov (United States)

    Gambarota, Giulio

    2017-07-15

    Magnetic resonance spectroscopy (MRS) is a well established modality for investigating tissue metabolism in vivo. In recent years, many efforts by the scientific community have been directed towards the improvement of metabolite detection and quantitation. Quantum mechanics simulations allow for investigations of the MR signal behaviour of metabolites; thus, they provide an essential tool in the optimization of metabolite detection. In this review, we will examine quantum mechanics simulations based on the density matrix formalism. The density matrix was introduced by von Neumann in 1927 to take into account statistical effects within the theory of quantum mechanics. We will discuss the main steps of the density matrix simulation of an arbitrary spin system and show some examples for the strongly coupled two spin system. Copyright © 2016 Elsevier Inc. All rights reserved.

  1. Quantum mechanics paradoxes at the Φ-factory

    International Nuclear Information System (INIS)

    Ghirardi, G.C.; Grassi, R.; Weber, T.

    1991-04-01

    We discuss the possibility of performing experiments allowing one to test quantum mechanics versus any local realistic model within the context of the physics at the Φ-factory. After having sketched the main features of the physical process under consideration and having focused the locality requirements for it, we derive Bell's inequality for the two-meson system. Comparison with quantum predictions shows that the inequality is not violated for any choice of the parameters characterizing the measurement process. Contrary to the case of spin variables, there is then no way to exclude, by experiments at the Φ-factory, the possibility of a local realistic description of the process. A recent suggestion about a test of quantum predictions versus the assumption of a spontaneous factorization mechanism, as well as the claimed validity of an inequality which is different from Bell's one, are also discussed. The general conclusion is that the Φ-factory facility does not seem to open new ways of testing quantum mechanics versus alternative general schemes of the type which are usually regarded as worth considering the debate about locality and quantum mechanics. The concluding Section is devoted to making clear our position with respect to the problems discussed in this paper. It is pointed out that, in our opinion, the existing experimental evidence makes already clear that one has to accept the ''mysterious'' features of microscopic systems. The really crucial problem is that of investigating whether one can restore a coherent worldview which generally conforms with our experience at the macroscopic level, by keeping all highly successful predictions of quantum theory at the microscopic one. (author). 22 refs

  2. Computing With Quantum Mechanical Oscillators

    National Research Council Canada - National Science Library

    Parks, A

    1991-01-01

    Despite the obvious practical considerations (e.g., stability, controllability), certain quantum mechanical systems seem to naturally lend themselves in a theoretical sense to the task of performing computations...

  3. Relativistic Brownian motion and the foundations of quantum mechanics

    International Nuclear Information System (INIS)

    Roy, S.

    1979-01-01

    Within the context of the generalized stochastic interpretation of quantum mechanics it is possible to deduce the quantum principles as well as to resolve the EPR paradox. Moreover, the postulates of the stochastic space-time as proposed by Frederick et al. can be deduced in a consistent way. A new possibility arises of rethinking of the existence of hidden variables in quantum mechanics

  4. Quantum mechanics concept assessment: Development and validation study

    Directory of Open Access Journals (Sweden)

    Homeyra R. Sadaghiani

    2015-03-01

    Full Text Available As part of an ongoing investigation of students’ learning in first semester upper-division quantum mechanics, we needed a high-quality conceptual assessment instrument for comparing outcomes of different curricular approaches. The process of developing such a tool started with converting a preliminary version of a 14-item open-ended quantum mechanics assessment tool (QMAT to a multiple-choice (MC format. Further question refinement, development of effective distractors, adding new questions, and robust statistical analysis has led to a 31-item quantum mechanics concept assessment (QMCA test. The QMCA is used as post-test only to assess students’ knowledge about five main topics of quantum measurement: the time-independent Schrödinger equation, wave functions and boundary conditions, time evolution, and probability density. During two years of testing and refinement, the QMCA has been given in alpha (N=61 and beta versions (N=263 to students in upper division quantum mechanics courses at 11 different institutions with an average post-test score of 54%. By allowing for comparisons of student learning across different populations and institutions, the QMCA provides instructors and researchers a more standard measure of effectiveness of different curricula or teaching strategies on student conceptual understanding of quantum mechanics. In this paper, we discuss the construction of effective distractors and the use of student interviews and expert feedback to revise and validate both questions and distractors. We include the results of common statistical tests of reliability and validity, which suggest the instrument is presently in a stable, usable, and promising form.

  5. Measurements and mathematical formalism of quantum mechanics

    Science.gov (United States)

    Slavnov, D. A.

    2007-03-01

    A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and functionals on this algebra (elementary states) associated with results of single measurements are used as primary components of the scheme. On the one hand, it is possible to use within the scheme the formalism of the standard (Kolmogorov) probability theory, and, on the other hand, it is possible to reproduce the mathematical formalism of standard quantum mechanics, and to study the limits of its applicability. A short outline is given of the necessary material from the theory of algebras and probability theory. It is described how the mathematical scheme of the paper agrees with the theory of quantum measurements, and avoids quantum paradoxes.

  6. Applications of supersymmetric quantum mechanics

    International Nuclear Information System (INIS)

    Rietdijk, R.H.

    1992-01-01

    The central subject of the thesis is the spinning particle model. It is a theory describing in a pseudoclassical way a Dirac particle which moves in an arbitrary d-dimensional space-time.In addition to space-time coordinates, the particle has spin which is described in terms of anti-commuting coordinates. Along the particles world line there is a super-symmetry between the fermionic spin variables and the bosonic position coordinates of the particle. It is straightforward to quantisize this model giving rise to supersymmetric quantum mechanics. The model does indeed describe a particle with spin 1/2, like a quark or an electron. There are two aspects of this model which is studied extensively in this thesis. First, to investigate the symmetries of the spinning particle on an arbitrary Riemannian manifold. Second, attention is drawn to the application of supersymmetric quantum mechanical models (i.e. spinning particle models) defined on an arbitrary Riemannian manifold to the calculation of anomalies in quantum field theories defined on the same manifold. (author). 49 refs.; 7 figs

  7. Quantum mechanics from elementary view

    International Nuclear Information System (INIS)

    Fischer, Karl

    2009-01-01

    This book offers an introduction to quantum mechanics as well as interesting supplements up to the beginnings of quantum field theory. A comprehensive mathematical block facilitates the access. It is rich on examples and otherwise mostly not findable calculations, which make it so transparent in its results. It likes the historical relations and brings so the feeling how much has been grown from the past. It brings also a short outline about relativity theory up to the understanding of the term ''metrics''. The spotlight holds the term product space, by means of which quantum mechanics is put together to a practicable theory. A simpler notation for instance at the Dirac equation facilitates also the understanding. On the mathematical side it is above all the term distributive law as well as the term linear combination, which lead so simple transparent definitions fast to more general. Generally it is tried to find an as possible elementary access to at least not elementary connections. So may it be for many both instructive and interesting

  8. Attosecond delays in photoionization: time and quantum mechanics

    International Nuclear Information System (INIS)

    Maquet, Alfred; Caillat, Jérémie; Taïeb, Richard

    2014-01-01

    This article addresses topics regarding time measurements performed on quantum systems. The motivation is linked to the advent of ‘attophysics’ which makes feasible to follow the motion of electrons in atoms and molecules, with time resolution at the attosecond (1 as = 10 −18 s) level, i.e. at the natural scale for electronic processes in these systems. In this context, attosecond ‘time-delays’ have been recently measured in experiments on photoionization and the question arises if such advances could cast a new light on the still active discussion on the status of the time variable in quantum mechanics. One issue still debatable is how to decide whether one can define a quantum time operator with eigenvalues associated to measurable ‘time-delays’, or time is a parameter, as it is implicit in the Newtonian classical mechanics. One objective of this paper is to investigate if the recent attophysics-based measurements could shed light on this parameter–operator conundrum. To this end, we present here the main features of the theory background, followed by an analysis of the experimental schemes that have been used to evidence attosecond ‘time-delays’ in photoionization. Our conclusion is that these results reinforce the view that time is a parameter which cannot be defined without reference to classical mechanics. (tutorial)

  9. Lectures on quantum mechanics with problems, exercises and their solutions

    CERN Document Server

    Basdevant, Jean-Louis

    2016-01-01

    The new edition of this remarkable text offers the reader a conceptually strong introduction to quantum mechanics, but goes beyond this to present a fascinating tour of modern theoretical physics. Beautifully illustrated and engagingly written, it starts with a brief overview of diverse topics across physics including nanotechnology, statistical physics, materials science, astrophysics, and cosmology. The core of the book covers both established and emerging aspects of quantum mechanics. A concise introduction to traditional quantum mechanics covers the Schrödinger equation, Hilbert space, the algebra of observables, hydrogen atom, spin and Pauli principle. Modern features of the field are presented by exploring entangled states, Bell's inequality, quantum cryptography, quantum teleportation and quantum mechanics in the universe. This new edition has been enchanced through the addition of numerous problems with detailed solutions, an introduction to the mathematical tools needed and expanded discussion of th...

  10. Quantum mechanical metastability: When and why?

    International Nuclear Information System (INIS)

    Boyanovsky, D.; Willey, R.; Holman, R.

    1992-01-01

    We study quantum mechanical metastability with an eye towards false vacuum decay. We point out some technical and conceptual problems with the familiar bounce treatment of this process. We illustrate with simple quantum mechanical examples that the bounce formalism fails to account for the correct boundary conditions. It is also shown, that the bounce approach overestimates the time scales for tunneling of localized packets in typical (slightly) biased double well potentials. We present a thorough WKB analysis with particular attention to semiclassical trajectories corresponding to complex saddle points. We point out that the boundary conditions determine the proper choice of saddle points and the bounce approach fails to account for semiclassical trajectories in many physically relevant cases. We recognize that these saddle points account for the matching conditions of the WKB wave functions beyond the barriers and restore unitarity and reality of eigenvalues for self-adjoint boundary conditions. We provide a novel approach to the semiclassical analysis of out of equilibrium decay in real time in quantum statistical mechanics. (orig.)

  11. Stochastic quantum mechanics and quantum spacetime

    International Nuclear Information System (INIS)

    Prugovecki, E.

    1984-01-01

    This monograph's principal intent is to provide a systematic and self-contained introduction to an alternative unification of relativity with quantum theory based on stochastic phase spaces and stochastic geometries, and presented at a level accessible to graduate students in theoretical and mathematical physics as well as to professional physicists and mathematicians. The proposed framework for unification embraces classical as well as quantum theories by implementing an epistemic idea first put forth by M. Born, namely that all physical theories should be formulated in terms of stochastic rather than deterministic values for measurable quantities. The framework gives rise to a whole range of yet unresearched problems, whose solutions are bound to shed some light on the relationship between relativity and quantum theories of the most fundamental physical and mathematical levels. (Auth.)

  12. Quantum mechanics by walking 1. Foundations; Quantenmechanik zu Fuss 1. Grundlagen

    Energy Technology Data Exchange (ETDEWEB)

    Pade, Jochen [Oldenburg Univ. (Germany)

    2012-11-01

    Quantum mechanics by walking introduces to the foundations of non-relativistic quantum mechanics. This book applies to studyings of teaching physics as well as all studyings of physics, who look for an appropriate, easy, fresh, and modern approach to the field. In the present first volume the essential principles of quantum mechanics are worked out. in order to be able to develop their mathematical formulation as fastly and clearly as possible, systematically between wave mechanics and algebraic presentation is changed. Beside themes, which are traditionally in textbooks of quantum mechanics, extensively actual aspects like interaction-free quantum measurement, neutrino oscillations, or quantum cryptography are considered as well as fundamental problems and epistemological questions discussed, as they occur in connection with the measurement process. The list of the postulates of quantum mechanics closes this volume; they form the framework for the extensions and applications, which are discussed in the second volume. The required mathematical aids are introduced step by step. In the appendix the most important mathematical tools are compactly collected, so that supplementing literature can be far reachingly abandoned. Furthermore in the appendix supplementing themes are deepened as for instance the Quantum Zeno effect or delayed-choice experiments.

  13. Para-bosons and Para-fermions in Quantum Mechanics

    International Nuclear Information System (INIS)

    Cattani, M.S.D.; Fernandes, N.C.

    1982-01-01

    Within the framework of the ordinary quantum mechanics, a detailed study of the energy eigenfunctions of N identical particles using the irreducible representations of the permutation group in the Hilbert space is performed. It is shown that the para-states, as occurs with the boson and fermion states, are compatible with the postulates of quantum mechanics and with the principle of indistinguishability. A mathematical support for the existence of para-bosons and para-fermions is given. Gentile's quantum statistics is, in a certain sense, justified. (Author) [pt

  14. Quantum mechanics on noncommutative spacetime

    International Nuclear Information System (INIS)

    Calmet, Xavier; Selvaggi, Michele

    2006-01-01

    We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect

  15. A full quantum analysis of the Stern–Gerlach experiment using the evolution operator method: analyzing current issues in teaching quantum mechanics

    International Nuclear Information System (INIS)

    Benítez Rodríguez, E; Aguilar, L M Arévalo; Martínez, E Piceno

    2017-01-01

    To the quantum mechanics specialists community it is a well-known fact that the famous original Stern–Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantum mechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantum mechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantum mechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community. (paper)

  16. Study of quantum spin correlations of relativistic electron pairs - Testing nonlocality of relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Bodek, K.; Rozpędzik, D.; Zejma, J.; Caban, P.; Rembieliński, J.; Włodarczyk, M.; Ciborowski, J.; Enders, J.; Köhler, A.; Kozela, A.

    2013-01-01

    The Polish-German project QUEST aims at studying relativistic quantum spin correlations of the Einstein-Rosen-Podolsky-Bohm type, through measurement of the correlation function and the corresponding probabilities for relativistic electron pairs. The results will be compared to theoretical predictions obtained by us within the framework of relativistic quantum mechanics, based on assumptions regarding the form of the relativistic spin operator. Agreement or divergence will be interpreted in the context of non-uniqueness of the relativistic spin operator in quantum mechanics as well as dependence of the correlation function on the choice of observables representing the spin. Pairs of correlated electrons will originate from the Mo/ller scattering of polarized 15 MeV electrons provided by the superconducting Darmstadt electron linear accelerator S-DALINAC, TU Darmstadt, incident on a Be target. Spin projections will be determined using the Mott polarimetry technique. Measurements (starting 2013) are planned for longitudinal and transverse beam polarizations and different orientations of the beam polarization vector w.r.t. the Mo/ller scattering plane. This is the first project to study relativistic spin correlations for particles with mass

  17. Quantum mechanical calculations related to ionization and charge transfer in DNA

    International Nuclear Information System (INIS)

    Cauët, E; Liévin, J; Valiev, M; Weare, J H

    2012-01-01

    Ionization and charge migration in DNA play crucial roles in mechanisms of DNA damage caused by ionizing radiation, oxidizing agents and photo-irradiation. Therefore, an evaluation of the ionization properties of the DNA bases is central to the full interpretation and understanding of the elementary reactive processes that occur at the molecular level during the initial exposure and afterwards. Ab initio quantum mechanical (QM) methods have been successful in providing highly accurate evaluations of key parameters, such as ionization energies (IE) of DNA bases. Hence, in this study, we performed high-level QM calculations to characterize the molecular energy levels and potential energy surfaces, which shed light on ionization and charge migration between DNA bases. In particular, we examined the IEs of guanine, the most easily oxidized base, isolated and embedded in base clusters, and investigated the mechanism of charge migration over two and three stacked guanines. The IE of guanine in the human telomere sequence has also been evaluated. We report a simple molecular orbital analysis to explain how modifications in the base sequence are expected to change the efficiency of the sequence as a hole trap. Finally, the application of a hybrid approach combining quantum mechanics with molecular mechanics brings an interesting discussion as to how the native aqueous DNA environment affects the IE threshold of nucleobases.

  18. Relativistic Brownian motion and the foundations of quantum mechanics

    International Nuclear Information System (INIS)

    Roy, S.

    1979-01-01

    Within the context of the generalized stochastic interpretation of quantum mechanics it is possible to deduce the quantum principles as well as to resolve the EPR paradox. Moreover, the postulates of the stochastic space-time as proposed by Frederick et al. can be deduced in a consistent way. A new possibility arises of rethinking of the existence of hidden variables in quantum mechanics. (author)

  19. The measurement problem in quantum mechanics: approximation to the phenomenon of decoherence by operational identities

    International Nuclear Information System (INIS)

    Usera, J.I.

    1996-01-01

    An approach based on bits and pieces of standard wisdom plus and operational quantum mechanical identity deduced by the author is presented here in order to convey arguments concerning the quantum theory of measurement and which betray a flavor against completive claims for quantum mechanics. Special emphasis is put on the phenomenon of decoherence. This phenomenon (which is experimentally verifiable) finds natural room within the formalism while the wave function collapse (which is not) is precluded. (Author)

  20. Hey to quantum mechanics: the Riesz-Fejer theorem

    International Nuclear Information System (INIS)

    Frohner, F. H.

    2000-01-01

    Quantum mechanics is spectacularly successful on the technical level but its rules remain mysterious, more than seventy years after its inception. The central question concerns the super-position principle, i. e. the rule to calculate probabilities as absolute squares of complex wave functions. Other questions concern the collapse of the wave function when new information becomes available, or the relationship between spin and statistics. These questions are reconsidered. The superposition principle turns out to be a consequence of an apparently little known mathematical theorem for non-negative Fourier polynomials published by Fejer in 1915 that implies wave-mechanical interference for all probability distributions. Combined with the classical Hamiltonian equations for free motion, gauge invariance and particle indistinguishability the theorem yields A basic features of quantum mechanics - wave-particle duality, operator calculus, uncertainty relations, Schrodinger equation, and quantum statistics. Bayesian updating of probabilities with new evidence, well known in probability theory, entails collapse of the wave function. Thus the Riesz-Fejer provides a key to a better understanding of quantum mechanics. (author)

  1. Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

    Science.gov (United States)

    Tsai, Hung-Ming; Poirier, Bill

    2016-03-01

    In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schrödinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantum mechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature—suggesting a “many interacting worlds” interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive and well-localized everywhere, and its spatial integral is conserved over time—in any inertial frame. Finally, the ensemble-averaged wavepacket motion is along a straight line path through spacetime. In this manner, the pathologies of the wave-based relativistic quantum theory, as applied to wavepacket propagation, are avoided.

  2. Quantum mechanical facets of chemical bonds

    International Nuclear Information System (INIS)

    Daudel, R.

    1976-01-01

    To define the concept of bond is both a central problem of quantum chemistry and a difficult one. The concept of bond appeared little by little in the mind of chemists from empirical observations. From the wave-mechanical viewpoint it is not an observable. Therefore there is no precise operator associated with that concept. As a consequence there is not a unique approach to the idea of chemical bond. This is why it is preferred to present various quantum mechanical facets, e.g. the energetic facet, the density facet, the partitioning facet and the functional facet, of that important concept. (Auth.)

  3. A deformation quantization theory for noncommutative quantum mechanics

    International Nuclear Information System (INIS)

    Costa Dias, Nuno; Prata, Joao Nuno; Gosson, Maurice de; Luef, Franz

    2010-01-01

    We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].

  4. On possibility of agreement of quantum mechanics with classical probability theory

    International Nuclear Information System (INIS)

    Slavnov, D.A.

    2006-01-01

    Paper describes a scheme to carry out a construction of the quantum mechanics where the quantum system is assumed to be a pattern of the open classical subsystems. It enables to make use both of the formal classical logic and the classical probability theory in the quantum mechanics. On the other hand, in terms of the mentioned approach one manages to ensure complete reconstruction of the quantum mechanics standard mathematical tool specifying its application limits. The problem dealing with the quantum state reduction is scrutinized [ru

  5. An adaptive quantum mechanics/molecular mechanics method for the infrared spectrum of water: incorporation of the quantum effect between solute and solvent.

    Science.gov (United States)

    Watanabe, Hiroshi C; Banno, Misa; Sakurai, Minoru

    2016-03-14

    Quantum effects in solute-solvent interactions, such as the many-body effect and the dipole-induced dipole, are known to be critical factors influencing the infrared spectra of species in the liquid phase. For accurate spectrum evaluation, the surrounding solvent molecules, in addition to the solute of interest, should be treated using a quantum mechanical method. However, conventional quantum mechanics/molecular mechanics (QM/MM) methods cannot handle free QM solvent molecules during molecular dynamics (MD) simulation because of the diffusion problem. To deal with this problem, we have previously proposed an adaptive QM/MM "size-consistent multipartitioning (SCMP) method". In the present study, as the first application of the SCMP method, we demonstrate the reproduction of the infrared spectrum of liquid-phase water, and evaluate the quantum effect in comparison with conventional QM/MM simulations.

  6. An introduction to the tomographic picture of quantum mechanics

    International Nuclear Information System (INIS)

    Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Ventriglia, F

    2009-01-01

    Starting from the famous Pauli problem on the possibility of associating quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e. tomographic probabilities) is reviewed in a pedagogical style. The relation between the quantum state description and the classical state description is elucidated. The difference between those sets of tomograms is described by inequalities equivalent to a complete set of uncertainty relations for the quantum domain and to non-negativity of probability density on phase space in the classical domain. The intersection of such sets is studied. The mathematical mechanism that allows us to construct different kinds of tomographic probabilities like symplectic tomograms, spin tomograms, photon number tomograms, etc is clarified and a connection with abstract Hilbert space properties is established. The superposition rule and uncertainty relations in terms of probabilities as well as quantum basic equations like quantum evolution and energy spectra equations are given in an explicit form. A method to check experimentally the uncertainty relations is suggested using optical tomograms. Entanglement phenomena and the connection with semigroups acting on simplexes are studied in detail for spin states in the case of two-qubits. The star-product formalism is associated with the tomographic probability formulation of quantum mechanics.

  7. Quantum thermodynamic cycles and quantum heat engines. II.

    Science.gov (United States)

    Quan, H T

    2009-04-01

    We study the quantum-mechanical generalization of force or pressure, and then we extend the classical thermodynamic isobaric process to quantum-mechanical systems. Based on these efforts, we are able to study the quantum version of thermodynamic cycles that consist of quantum isobaric processes, such as the quantum Brayton cycle and quantum Diesel cycle. We also consider the implementation of the quantum Brayton cycle and quantum Diesel cycle with some model systems, such as single particle in a one-dimensional box and single-mode radiation field in a cavity. These studies lay the microscopic (quantum-mechanical) foundation for Szilard-Zurek single-molecule engine.

  8. A pseudobond parametrization for improved electrostatics in quantum mechanical/molecular mechanical simulations of enzymes.

    Science.gov (United States)

    Parks, Jerry M; Hu, Hao; Cohen, Aron J; Yang, Weitao

    2008-10-21

    The pseudobond method is used in quantum mechanical/molecular mechanical (QM/MM) simulations in which a covalent bond connects the quantum mechanical and classical subsystems. In this method, the molecular mechanical boundary atom is replaced by a special quantum mechanical atom with one free valence that forms a bond with the rest of the quantum mechanical subsystem. This boundary atom is modified through the use of a parametrized effective core potential and basis set. The pseudobond is designed to reproduce the properties of the covalent bond that it has replaced, while invoking as small a perturbation as possible on the system. Following the work of Zhang [J. Chem. Phys. 122, 024114 (2005)], we have developed new pseudobond parameters for use in the simulation of enzymatic systems. Our parameters yield improved electrostatics and deprotonation energies, while at the same time maintaining accurate geometries. We provide parameters for C(ps)(sp(3))-C(sp(3)), C(ps)(sp(3))-C(sp(2),carbonyl), and C(ps)(sp(3))-N(sp(3)) pseudobonds, which allow the interface between the quantum mechanical and molecular mechanical subsystems to be constructed at either the C(alpha)-C(beta) bond of a given amino acid residue or along the peptide backbone. In addition, we demonstrate the efficiency of our parametrization method by generating residue-specific pseudobond parameters for a single amino acid. Such an approach may enable higher accuracy than general purpose parameters for specific QM/MM applications.

  9. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode.

    Science.gov (United States)

    Verhagen, E; Deléglise, S; Weis, S; Schliesser, A; Kippenberg, T J

    2012-02-01

    Optical laser fields have been widely used to achieve quantum control over the motional and internal degrees of freedom of atoms and ions, molecules and atomic gases. A route to controlling the quantum states of macroscopic mechanical oscillators in a similar fashion is to exploit the parametric coupling between optical and mechanical degrees of freedom through radiation pressure in suitably engineered optical cavities. If the optomechanical coupling is 'quantum coherent'--that is, if the coherent coupling rate exceeds both the optical and the mechanical decoherence rate--quantum states are transferred from the optical field to the mechanical oscillator and vice versa. This transfer allows control of the mechanical oscillator state using the wide range of available quantum optical techniques. So far, however, quantum-coherent coupling of micromechanical oscillators has only been achieved using microwave fields at millikelvin temperatures. Optical experiments have not attained this regime owing to the large mechanical decoherence rates and the difficulty of overcoming optical dissipation. Here we achieve quantum-coherent coupling between optical photons and a micromechanical oscillator. Simultaneously, coupling to the cold photon bath cools the mechanical oscillator to an average occupancy of 1.7 ± 0.1 motional quanta. Excitation with weak classical light pulses reveals the exchange of energy between the optical light field and the micromechanical oscillator in the time domain at the level of less than one quantum on average. This optomechanical system establishes an efficient quantum interface between mechanical oscillators and optical photons, which can provide decoherence-free transport of quantum states through optical fibres. Our results offer a route towards the use of mechanical oscillators as quantum transducers or in microwave-to-optical quantum links.

  10. Hamiltonian and physical Hilbert space in polymer quantum mechanics

    International Nuclear Information System (INIS)

    Corichi, Alejandro; Vukasinac, Tatjana; Zapata, Jose A

    2007-01-01

    In this paper, a version of polymer quantum mechanics, which is inspired by loop quantum gravity, is considered and shown to be equivalent, in a precise sense, to the standard, experimentally tested Schroedinger quantum mechanics. The kinematical cornerstone of our framework is the so-called polymer representation of the Heisenberg-Weyl (HW) algebra, which is the starting point of the construction. The dynamics is constructed as a continuum limit of effective theories characterized by a scale, and requires a renormalization of the inner product. The result is a physical Hilbert space in which the continuum Hamiltonian can be represented and that is unitarily equivalent to the Schroedinger representation of quantum mechanics. As a concrete implementation of our formalism, the simple harmonic oscillator is fully developed

  11. The connection of two-particle relativistic quantum mechanics with the Bethe-Salpeter equation

    International Nuclear Information System (INIS)

    Sazdjian, H.

    1986-02-01

    We show the formal equivalence between the wave equations of two-particle relativistic quantum mechanics, based on the manifestly covariant hamiltonian formalism with constraints, and the Bethe-Salpeter equation. This is achieved by algebraically transforming the latter so as to separate it into two independent equations which match the equations of hamiltonian relativistic quantum mechanics. The first equation determines the relative time evolution of the system, while the second one yields a three-dimensional eigenvalue equation. A connection is thus established between the Bethe-Salpeter wave function and its kernel on the one hand and the quantum mechanical wave function and interaction potential on the other. For the sector of solutions of the Bethe-Salpeter equation having non-relativistic limits, this relationship can be evaluated in perturbation theory. We also device a generalized form of the instantaneous approximation which simplifies the various expressions involved in the above relations. It also permits the evaluation of the normalization condition of the quantum mechanical wave function as a three-dimensional integral

  12. Quantum mechanics of electromagnetically bounded spin-1/2 particles in an expanding universe

    International Nuclear Information System (INIS)

    Audretsch, J.; Schaefer, G.

    1978-01-01

    The quantum mechanically described electron in an external electromagnetic field, both embedded in an expanding universe with shear, is discussed. This is important for the fundamental question as to whether a quantum mechanically treated atomic clock in curved space-time (based on a hydrogen atom) shows proper or gravitational time. Contradictory results reported by other authors seem to imply that quantum mechanics cannot be reconciled with curved space-time. It is shown that this is not the case for expanding Robertson-Walker universes. A Hilbert space formulation of the problem with special regard to the Hamiltonian is given. The respective influence of the cosmic expansion and the intrinsic and extrinsic curvatures of the cosmic hypersurfaces on bound quantum mechanical systems is treated in general. For the special case of an expanding 3-flat (epsilon= 0) Robertson-Walker universe it is shown that the energy levels of a hydrogen atom agree completely with the one in 4-flat space-time, so that in this case the hydrogen atom can be taken as atomic clock showing proper time. (author)

  13. Performance assessment of semiempirical molecular orbital methods in describing halogen bonding: quantum mechanical and quantum mechanical/molecular mechanical-molecular dynamics study.

    Science.gov (United States)

    Ibrahim, Mahmoud A A

    2011-10-24

    The performance of semiempirical molecular-orbital methods--MNDO, MNDO-d, AM1, RM1, PM3 and PM6--in describing halogen bonding was evaluated, and the results were compared with molecular mechanical (MM) and quantum mechanical (QM) data. Three types of performance were assessed: (1) geometrical optimizations and binding energy calculations for 27 halogen-containing molecules complexed with various Lewis bases (Two of the tested methods, AM1 and RM1, gave results that agree with the QM data.); (2) charge distribution calculations for halobenzene molecules, determined by calculating the solvation free energies of the molecules relative to benzene in explicit and implicit generalized Born (GB) solvents (None of the methods gave results that agree with the experimental data.); and (3) appropriateness of the semiempirical methods in the hybrid quantum-mechanical/molecular-mechanical (QM/MM) scheme, investigated by studying the molecular inhibition of CK2 protein by eight halobenzimidazole and -benzotriazole derivatives using hybrid QM/MM molecular-dynamics (MD) simulations with the inhibitor described at the QM level by the AM1 method and the rest of the system described at the MM level. The pure MM approach with inclusion of an extra point of positive charge on the halogen atom approach gave better results than the hybrid QM/MM approach involving the AM1 method. Also, in comparison with the pure MM-GBSA (generalized Born surface area) binding energies and experimental data, the calculated QM/MM-GBSA binding energies of the inhibitors were improved by replacing the G(GB,QM/MM) solvation term with the corresponding G(GB,MM) term.

  14. An objective interpretation of Lagrangian quantum mechanics

    International Nuclear Information System (INIS)

    Roberts, K.V.

    1978-01-01

    Unlike classical mechanics, the Copenhagen interpretation of quantum mechanics does not provide an objective space-time picture of the actual history of a physical system. This paper suggests how the conceptual foundations of quantum mechanics can be reformulated, without changing the mathematical content of the theory or its detailed agreement with experiment and without introducing any hidden variables, in order to provide an objective, covariant, Lagrangian description of reality which is deterministic and time-symmetric on the microscopic scale. The basis of this description can be expressed either as an action functional or as a summation over Feynman diagrams or paths. The probability laws associated with the quantum-mechanical measurement process, and the asymmetry in time of the principles of macroscopic causality and of the laws of statistical mechanics, are interpreted as consequences of the particular boundary conditions that apply to the actual universe. The objective interpretation does not include the observer and the measurement process among the fundamental concepts of the theory, but it does not entail a revision of the ideas of determinism and of time, since in a Lagrangian theory both initial and final boundary conditions on the action functional are required. (author)

  15. Holomorphic anomaly and quantum mechanics

    Science.gov (United States)

    Codesido, Santiago; Mariño, Marcos

    2018-02-01

    We show that the all-orders WKB periods of one-dimensional quantum mechanical oscillators are governed by the refined holomorphic anomaly equations of topological string theory. We analyze in detail the double-well potential and the cubic and quartic oscillators, and we calculate the WKB expansion of their quantum free energies by using the direct integration of the anomaly equations. We reproduce in this way all known results about the quantum periods of these models, which we express in terms of modular forms on the WKB curve. As an application of our results, we study the large order behavior of the WKB expansion in the case of the double well, which displays the double factorial growth typical of string theory.

  16. Erwin Schroedinger, Philosophy and the birth of quantum mechanics

    International Nuclear Information System (INIS)

    Bitbol, M.; Darrigol, O.

    1992-01-01

    The purpose of this collection of articles is to highlight the relation between Schroedinger's less well known research and his thoughts on quantum mechanics: philosophy, statistical mechanics, general relativity, cosmology, unified field theories, etc. Some articles are devoted to contemporary extensions of his work, and in particular on current echoes of his interpretation of quantum mechanics

  17. A Time-Space Symmetry Based Cylindrical Model for Quantum Mechanical Interpretations

    Science.gov (United States)

    Vo Van, Thuan

    2017-12-01

    Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time-space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space-time curvatures. Interpretation of some important issues of quantum mechanical reality is carried out in comparison with the 5D space-time-matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally.

  18. Molecular recognition of the environment and mechanisms of the origin of species in quantum-like modeling of evolution.

    Science.gov (United States)

    Melkikh, Alexey V; Khrennikov, Andrei

    2017-11-01

    A review of the mechanisms of speciation is performed. The mechanisms of the evolution of species, taking into account the feedback of the state of the environment and mechanisms of the emergence of complexity, are considered. It is shown that these mechanisms, at the molecular level, cannot work steadily in terms of classical mechanics. Quantum mechanisms of changes in the genome, based on the long-range interaction potential between biologically important molecules, are proposed as one of possible explanation. Different variants of interactions of the organism and environment based on molecular recognition and leading to new species origins are considered. Experiments to verify the model are proposed. This bio-physical study is completed by the general operational model of based on quantum information theory. The latter is applied to model of epigenetic evolution. We briefly present the basics of the quantum-like approach to modeling of bio-informational processes. This approach is illustrated by the quantum-like model of epigenetic evolution. Copyright © 2017 Elsevier Ltd. All rights reserved.

  19. Faster than Hermitian Quantum Mechanics

    International Nuclear Information System (INIS)

    Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.; Meister, Bernhard K.

    2007-01-01

    Given an initial quantum state vertical bar ψ I > and a final quantum state vertical bar ψ F >, there exist Hamiltonians H under which vertical bar ψ I > evolves into vertical bar ψ F >. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of H is held fixed, which H achieves this transformation in the least time τ? For Hermitian Hamiltonians τ has a nonzero lower bound. However, among non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint, τ can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from vertical bar ψ I > to vertical bar ψ F > can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if they are connected by a wormhole. This result may have applications in quantum computing

  20. Introduction to quantum statistical mechanics

    CERN Document Server

    Bogolyubov, N N

    2010-01-01

    Introduction to Quantum Statistical Mechanics (Second Edition) may be used as an advanced textbook by graduate students, even ambitious undergraduates in physics. It is also suitable for non experts in physics who wish to have an overview of some of the classic and fundamental quantum models in the subject. The explanation in the book is detailed enough to capture the interest of the reader, and complete enough to provide the necessary background material needed to dwell further into the subject and explore the research literature.

  1. Student Understanding of Time Dependence in Quantum Mechanics

    Science.gov (United States)

    Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

    2015-01-01

    The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…

  2. Insights into Teaching Quantum Mechanics in Secondary and Lower Undergraduate Education

    Science.gov (United States)

    Krijtenburg-Lewerissa, K.; Pol, H. J.; Brinkman, A.; van Joolingen, W. R.

    2017-01-01

    This study presents a review of the current state of research on teaching quantum mechanics in secondary and lower undergraduate education. A conceptual approach to quantum mechanics is being implemented in more and more introductory physics courses around the world. Because of the differences between the conceptual nature of quantum mechanics and…

  3. The metaphysics of quantum mechanics: Modal interpretations

    Science.gov (United States)

    Gluck, Stuart Murray

    2004-11-01

    This dissertation begins with the argument that a preferred way of doing metaphysics is through philosophy of physics. An understanding of quantum physics is vital to answering questions such as: What counts as an individual object in physical ontology? Is the universe fundamentally indeterministic? Are indiscernibles identical? This study explores how the various modal interpretations of quantum mechanics answer these sorts of questions; modal accounts are one of the two classes of interpretations along with so-called collapse accounts. This study suggests a new alternative within the class of modal views that yields a more plausible ontology, one in which the Principle of the Identity of Indisceribles is necessarily true. Next, it shows that modal interpretations can consistently deny that the universe must be fundamentally indeterministic so long as they accept certain other metaphysical commitments: either a perfect initial distribution of states in the universe or some form of primitive dispositional properties. Finally, the study sketches out a future research project for modal interpretations based on developing quantified quantum logic.

  4. More on homological supersymmetric quantum mechanics

    Science.gov (United States)

    Behtash, Alireza

    2018-03-01

    In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory. We briefly touch on the exact non-BPS solutions of the bosonized supersymmetric quantum mechanics on algebraic geometric grounds and report that their complex phases can be accessed through the cohomology of WKB 1-form of the underlying singular spectral curve subject to necessary cohomological corrections for nonzero genus. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of N =4 quantum mechanics with background R -symmetry gauge fields. We conjecture that certain symmetries of the refined Witten index and singularities of the moduli space may be used to determine the correct intersection coefficients. A few examples, where this conjecture holds, are shown in both linear and closed quivers with rank-one quiver gauge groups. The R -anomaly removal along the "Morsified" relative homology cycles also called "Lefschetz thimbles" is shown to lead to the appearance of Stokes lines. We show that the Fayet-Iliopoulos parameters appear in the intersection coefficients for the relative homology of the quiver quantum mechanics resulting from dimensional reduction of 2 d N =(2 ,2 ) gauge theory on a circle and explicitly calculate integrals along the Lefschetz thimbles in N =4 C Pk -1 model. The Stokes jumping of coefficients and its relation to wall crossing phenomena is briefly discussed. We also find that the notion of "on-the-wall" index is related to the invariant Lefschetz thimbles under Stokes phenomena. An implication of the Lefschetz thimbles in constructing knots from quiver quantum mechanics is indicated.

  5. How to recover Newtonian mechanics from non-relative quantum mechanics in limit ℎ→0

    International Nuclear Information System (INIS)

    Mei Shizhong

    2001-01-01

    It is assumed that when ℎ→0, correct non-relative quantum mechanics should be equivalent to Newtonian mechanics. Starting from this point, the authors slightly revised the widely accepted non-relative quantum mechanics such that the mechanics after modification is strictly equivalent to that before the modification when ℎ≠0, and equivalent to Newtonian mechanics in the limit ℎ→0. The significance lies in the possibility that if authors further postulate that corrected relative quantum mechanics is equivalent to Einstein's theory of relativity in the case ℎ→0, then authors may obtain different predictions from what produced by the former that will help to verify or improve it

  6. Quantum Mechanical Studies of DNA and LNA

    DEFF Research Database (Denmark)

    Koch, Troels; Shim, Irene; Lindow, Morten

    2014-01-01

    Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies of the e......Quantum mechanical (QM) methodology has been employed to study the structure activity relations of DNA and locked nucleic acid (LNA). The QM calculations provide the basis for construction of molecular structure and electrostatic surface potentials from molecular orbitals. The topologies...

  7. Quantum mechanics new approaches to selected topics

    CERN Document Server

    Lipkin, Harry Jeannot

    1973-01-01

    Acclaimed as ""excellent"" (Nature) and ""very original and refreshing"" (Physics Today), this collection of self-contained studies is geared toward advanced undergraduates and graduate students. Its broad selection of topics includes the Mössbauer effect, many-body quantum mechanics, scattering theory, Feynman diagrams, and relativistic quantum mechanics.Author Harry J. Lipkin, a well-known teacher at Israel's Weizmann Institute, takes an unusual approach by introducing many interesting physical problems and mathematical techniques at a much earlier point than in conventional texts. This meth

  8. Uncertainty and complementarity in axiomatic quantum mechanics

    International Nuclear Information System (INIS)

    Lahti, P.J.

    1980-01-01

    An investigation of the uncertainty principle and the complementarity principle is carried through. The physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation of the theory. Two extra axioms are stated, reflecting the ideas of the uncertainty principle and the complementarity principle, respectively. The quantal features of these axioms are explicated. (author)

  9. Supersymmetric quantum mechanics under point singularities

    International Nuclear Information System (INIS)

    Uchino, Takashi; Tsutsui, Izumi

    2003-01-01

    We provide a systematic study on the possibility of supersymmetry (SUSY) for one-dimensional quantum mechanical systems consisting of a pair of lines R or intervals [-l, l] each having a point singularity. We consider the most general singularities and walls (boundaries) at x = ±l admitted quantum mechanically, using a U(2) family of parameters to specify one singularity and similarly a U(1) family of parameters to specify one wall. With these parameter freedoms, we find that for a certain subfamily the line systems acquire an N = 1 SUSY which can be enhanced to N = 4 if the parameters are further tuned, and that these SUSY are generically broken except for a special case. The interval systems, on the other hand, can accommodate N = 2 or N = 4 SUSY, broken or unbroken, and exhibit a rich variety of (degenerate) spectra. Our SUSY systems include the familiar SUSY systems with the Dirac δ(x)-potential, and hence are extensions of the known SUSY quantum mechanics to those with general point singularities and walls. The self-adjointness of the supercharge in relation to the self-adjointness of the Hamiltonian is also discussed

  10. Quantum KAM technique and Yang endash Mills quantum mechanics

    International Nuclear Information System (INIS)

    Halperin, I.

    1995-01-01

    We study a quantum analogue of the iterative perturbation theory by Kolmogorov used in the proof of the Kolmogorov endash Arnold endash Moser (KAM) theorem. The method is based on sequent canonical transformations with a open-quote open-quote running close-quote close-quote coupling constant λ, λ 2 , λ 4 , etc. The proposed scheme, as its classical predecessor, is open-quote open-quote superconvergent close-quote close-quote in the sense that after the nth step, a theory is solved to the accuracy of order λ 2n-1 . It is shown that the Kolmogorov technique corresponds to an infinite resummation of the usual perturbative series. The corresponding expansion is convergent for the quantum anharmonic oscillator due to the fact that it turns out to be identical to the Pade series. The method is easily generalizable to many-dimensional cases. The Kolmogorov technique is further applied to a non-perturbative treatment of Yang endash Mills quantum mechanics. A controllable expansion for the wave function near the origin is constructed. For large fields, we build an asymptotic adiabatic expansion in inverse powers of the field. This asymptotic solution contains arbitrary constants which are not fixed by the boundary conditions at infinity. To find them, we approximately match the two expansions in an intermediate region. We also discuss some analogies between this problem and the method of QCD sum rules. Copyright copyright 1995 Academic Press, Inc

  11. A signed particle formulation of non-relativistic quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg

    2015-09-15

    A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schrödinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.

  12. The probabilistic roots of the quantum mechanical paradoxes

    International Nuclear Information System (INIS)

    Accardi, L.

    1984-01-01

    The goal of any mathematical investigation on the foundations of a physical theory is to clarify to what extent the mathematical formalism of that theory is uniquely determined by some clearly and explicitly stated physical assumptions. The achievement of that goal is particularly relevant in the case of the quantum theory. That with quantum theory a new kind of probability theory was involved, was clear since the very beginnings of quantum mechanics, even if it was not so clear which of the axioms of classical probability had to be substituted, which physically meaningful statement had to replace it, how and if a physically meaningful statement could justify the apparently strange quantum mechanical formalism. The lack of clear answers to these questions had a tremendous impact on the process of interpretation and misinterpretation of quantum theory. The attempts to answer these questions motivated the development of a new branch of probability theory - quantum probability - and led to definite mathematical answers to these questions. The author discusses how these mathematical results allow to solve in a rather natural way some old problems concerning the interpretation of quantum theory and its mathematical foundations. (Auth.)

  13. Quantum mechanical modeling the emission pattern and polarization of nanoscale light emitting diodes.

    Science.gov (United States)

    Wang, Rulin; Zhang, Yu; Bi, Fuzhen; Frauenheim, Thomas; Chen, GuanHua; Yam, ChiYung

    2016-07-21

    Understanding of the electroluminescence (EL) mechanism in optoelectronic devices is imperative for further optimization of their efficiency and effectiveness. Here, a quantum mechanical approach is formulated for modeling the EL processes in nanoscale light emitting diodes (LED). Based on non-equilibrium Green's function quantum transport equations, interactions with the electromagnetic vacuum environment are included to describe electrically driven light emission in the devices. The presented framework is illustrated by numerical simulations of a silicon nanowire LED device. EL spectra of the nanowire device under different bias voltages are obtained and, more importantly, the radiation pattern and polarization of optical emission can be determined using the current approach. This work is an important step forward towards atomistic quantum mechanical modeling of the electrically induced optical response in nanoscale systems.

  14. Quantum mechanics

    CERN Document Server

    Mandl, Franz

    1992-01-01

    The Manchester Physics Series General Editors: D. J. Sandiford; F. Mandl; A. C. Phillips Department of Physics and Astronomy, University of Manchester Properties of Matter B. H. Flowers and E. Mendoza Optics Second Edition F. G. Smith and J. H. Thomson Statistical Physics Second Edition F. Mandl Electromagnetism Second Edition I. S. Grant and W. R. Phillips Statistics R. J. Barlow Solid State Physics Second Edition J. R. Hook and H. E. Hall Quantum Mechanics F. Mandl Particle Physics Second Edition B. R. Martin and G. Shaw The Physics of Stars Second Edition A. C. Phillips Computing for Scient

  15. Mathematical sense-making in quantum mechanics: An initial peek

    Science.gov (United States)

    Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

    2017-12-01

    Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.

  16. Quantum mechanics principles and formalism

    CERN Document Server

    McWeeny, Roy

    2012-01-01

    Focusing on main principles of quantum mechanics and their immediate consequences, this graduate student-oriented volume develops the subject as a fundamental discipline, opening with review of origins of Schrödinger's equations and vector spaces.

  17. Quantum Mechanical Study of Nanoscale MOSFET

    Science.gov (United States)

    Svizhenko, Alexei; Anantram, M. P.; Govindan, T. R.; Biegel, Bryan

    2001-01-01

    The steady state characteristics of MOSFETS that are of practical Interest are the drive current, off-current, dope of drain current versus drain voltage, and threshold voltage. In this section, we show that quantum mechanical simulations yield significantly different results from drift-diffusion based methods. These differences arise because of the following quantum mechanical features: (I) polysilicon gate depletion in a manner opposite to the classical case (II) dependence of the resonant levels in the channel on the gate voltage, (III) tunneling of charge across the gate oxide and from source to drain, (IV) quasi-ballistic flow of electrons. Conclusions dI/dV versus V does not increase in a manner commensurate with the increase in number of subbands. - The increase in dI/dV with bias is much smaller then the increase in the number of subbands - a consequence of bragg reflection. Our calculations show an increase in transmission with length of contact, as seen in experiments. It is desirable for molecular electronics applications to have a small contact area, yet large coupling. In this case, the circumferential dependence of the nanotube wave function dictates: - Transmission in armchair tubes saturates around unity - Transmission in zigzag tubes saturates at two.

  18. Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects

    International Nuclear Information System (INIS)

    Santos Coelho, Leandro dos; Mariani, Viviana Cocco

    2008-01-01

    Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature

  19. Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects

    Energy Technology Data Exchange (ETDEWEB)

    dos Santos Coelho, Leandro [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil); Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)

    2008-11-15

    Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature. (author)

  20. Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects

    Energy Technology Data Exchange (ETDEWEB)

    Santos Coelho, Leandro dos [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: leandro.coelho@pucpr.br; Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: viviana.mariani@pucpr.br

    2008-11-15

    Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature.

  1. Supersymmetric quantum mechanics in three-dimensional space, 1

    International Nuclear Information System (INIS)

    Ui, Haruo

    1984-01-01

    As a direct generalization of the model of supersymmetric quantum mechanics by Witten, which describes the motion of a spin one-half particle in the one-dimensional space, we construct a model of the supersymmetric quantum mechanics in the three-dimensional space, which describes the motion of a spin one-half particle in central and spin-orbit potentials in the context of the nonrelativistic quantum mechanics. With the simplest choice of the (super) potential, this model is shown to reduce to the model of the harmonic oscillator plus constant spin-orbit potential of unit strength of both positive and negative signs, which was studied in detail in our recent paper in connection with ''accidental degeneracy'' as well as the ''graded groups''. This simplest model is discussed in some detail as an example of the three-dimensional supersymmetric quantum mechanical system, where the supersymmetry is an exact symmetry of the system. More general choice of a polynomial superpotential is also discussed. It is shown that the supersymmetry cannot be spontaneously broken for any polynomial superpotential in our three-dimensional model; this result is contrasted to the corresponding one in the one-dimensional model. (author)

  2. Challenges in large scale quantum mechanical calculations: Challenges in large scale quantum mechanical calculations

    Energy Technology Data Exchange (ETDEWEB)

    Ratcliff, Laura E. [Argonne Leadership Computing Facility, Argonne National Laboratory, Lemon IL USA; Mohr, Stephan [Department of Computer Applications in Science and Engineering, Barcelona Supercomputing Center (BSC-CNS), Barcelona Spain; Huhs, Georg [Department of Computer Applications in Science and Engineering, Barcelona Supercomputing Center (BSC-CNS), Barcelona Spain; Deutsch, Thierry [University Grenoble Alpes, INAC-MEM, Grenoble France; CEA, INAC-MEM, Grenoble France; Masella, Michel [Laboratoire de Biologie Structurale et Radiologie, Service de Bioénergétique, Biologie Structurale et Mécanisme, Institut de Biologie et de Technologie de Saclay, CEA Saclay, Gif-sur-Yvette Cedex France; Genovese, Luigi [University Grenoble Alpes, INAC-MEM, Grenoble France; CEA, INAC-MEM, Grenoble France

    2016-11-07

    During the past decades, quantum mechanical methods have undergone an amazing transition from pioneering investigations of experts into a wide range of practical applications, made by a vast community of researchers. First principles calculations of systems containing up to a few hundred atoms have become a standard in many branches of science. The sizes of the systems which can be simulated have increased even further during recent years, and quantum-mechanical calculations of systems up to many thousands of atoms are nowadays possible. This opens up new appealing possibilities, in particular for interdisciplinary work, bridging together communities of different needs and sensibilities. In this review we will present the current status of this topic, and will also give an outlook on the vast multitude of applications, challenges and opportunities stimulated by electronic structure calculations, making this field an important working tool and bringing together researchers of many different domains.

  3. A consistent interpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Omnes, Roland

    1990-01-01

    Some mostly recent theoretical and mathematical advances can be linked together to yield a new consistent interpretation of quantum mechanics. It relies upon a unique and universal interpretative rule of a logical character which is based upon Griffiths consistent history. Some new results in semi-classical physics allow classical physics to be derived from this rule, including its logical aspects, and to prove accordingly the existence of determinism within the quantum framework. Together with decoherence, this can be used to retrieve the existence of facts, despite the probabilistic character of the theory. Measurement theory can then be made entirely deductive. It is accordingly found that wave packet reduction is a logical property, whereas one can always choose to avoid using it. The practical consequences of this interpretation are most often in agreement with the Copenhagen formulation but they can be proved never to give rise to any logical inconsistency or paradox. (author)

  4. Singular potentials in quantum mechanics

    International Nuclear Information System (INIS)

    Aguilera-Navarro, V.C.; Koo, E. Ley

    1995-10-01

    This paper is a review of some mathematical methods as recently developed and applied to deal with singular potentials in Quantum Mechanics. Regular and singular perturbative methods as well as variational treatments are considered. (author). 25 refs

  5. Theory of “Weak Value" and Quantum Mechanical Measurements

    OpenAIRE

    Shikano, Yutaka

    2012-01-01

    Comment: to be published from "Measurements in Quantum Mechanics", edited by M. R. Pahlavani (InTech, 2012) Chapter 4 page 75. Yutaka Shikano (2012). ISBN: 978-953-51-0058-4 Available from: http://www.intechopen.com/articles/show/title/theory-of-weak-value-and-quantum-mechanical-measurement

  6. In Defense of a Heuristic Interpretation of Quantum Mechanics

    Science.gov (United States)

    Healy, Eamonn F.

    2010-01-01

    Although the presentation of quantum mechanics found in traditional textbooks is intellectually well founded, it suffers from a number of deficiencies. Specifically introducing quantum mechanics as a solution to the arcane dilemma, the ultraviolet catastrophe, does little to impress a nonscientific audience of the tremendous paradigmatic shift…

  7. Philosophic foundations of quantum mechanics

    CERN Document Server

    Reichenbach, Hans

    1998-01-01

    Physics concerns direct analysis of the physical world, while philosophy analyzes knowledge about the physical world. This volume combines both disciplines for a philosophical interpretation of quantum physics - an interpretation free from the imprecision of metaphysics, offering a view of the atomic world and its quantum mechanical results as concrete as the visible everyday world.Written by an internationally renowned philosopher who specialized in symbolic logic and the theory of relativity, this approach consists of three parts. The first section, which requires no background in math or p

  8. Operator methods in quantum mechanics

    CERN Document Server

    Schechter, Martin

    2003-01-01

    This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing q

  9. Quantum robots and quantum computers

    Energy Technology Data Exchange (ETDEWEB)

    Benioff, P.

    1998-07-01

    Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and systems that carry out experiments. The description of quantum computers is under active development. No description of systems to carry out experiments has been given. A small step in this direction is taken here by giving a description of quantum robots as mobile systems with on board quantum computers that interact with different environments. Some properties of these systems are discussed. A specific model based on the literature descriptions of quantum Turing machines is presented.

  10. Group Theoretical Approach for Controlled Quantum Mechanical Systems

    National Research Council Canada - National Science Library

    Tarn, Tzyh-Jong

    2007-01-01

    The aim of this research is the study of controllability of quantum mechanical systems and feedback control of de-coherence in order to gain an insight on the structure of control of quantum systems...

  11. Can quantum mechanics be an emergent phenomenon?

    Science.gov (United States)

    Blasone, Massimo; Jizba, Petr; Scardigli, Fabio

    2009-06-01

    We raise the issue whether conventional quantum mechanics, which is not a hidden variable theory in the usual Jauch-Piron's sense, might nevertheless be a hidden variable theory in the sense recently conjectured by G. 't Hooft in his pre-quantization scheme. We find that quantum mechanics might indeed have a fully deterministic underpinning by showing that Born's rule naturally emerges (i.e., it is not postulated) when 't Hooft's Hamiltonian for be-ables is combined with Koopmann-von Neumann operatorial formulation of classical physics.

  12. Can quantum mechanics be an emergent phenomenon?

    International Nuclear Information System (INIS)

    Blasone, Massimo; Jizba, Petr; Scardigli, Fabio

    2009-01-01

    We raise the issue whether conventional quantum mechanics, which is not a hidden variable theory in the usual Jauch-Piron's sense, might nevertheless be a hidden variable theory in the sense recently conjectured by G. 't Hooft in his pre-quantization scheme. We find that quantum mechanics might indeed have a fully deterministic underpinning by showing that Born's rule naturally emerges (i.e., it is not postulated) when 't Hooft's Hamiltonian for be-ables is combined with Koopmann-von Neumann operatorial formulation of classical physics.

  13. Making sense of quantum mechanics

    CERN Document Server

    Bricmont, Jean

    2016-01-01

    This book explains, in simple terms, with a minimum of mathematics, why things can appear to be in two places at the same time, why  correlations between simultaneous events occurring far apart cannot be explained by local mechanisms, and why, nevertheless, the quantum theory can be understood in terms of matter in motion. No need to worry, as some people do, whether a cat can be both dead and alive, whether the moon is there when nobody looks at it, or whether quantum systems need an observer to acquire definite properties. The author’s inimitable and even humorous style makes the book a pleasure to read while bringing a new clarity to many of the longstanding puzzles of quantum physics.

  14. Reflections on Friction in Quantum Mechanics

    Directory of Open Access Journals (Sweden)

    Yair Rezek

    2010-08-01

    Full Text Available Distinctly quantum friction effects of three types are surveyed: internalfriction, measurement-induced friction, and quantum-fluctuation-induced friction. We demonstrate that external driving will lead to quantum internal friction, and critique the measurement-based interpretation of friction. We conclude that in general systems will experience internal and external quantum friction over and beyond the classical frictional contributions.

  15. Time in quantum mechanics. Vol. 1. 2. ed.

    International Nuclear Information System (INIS)

    Muga, J.G.; Sala Mayato, R.; Egusquiza, I.L.

    2008-01-01

    The treatment of time in quantum mechanics is still an important and challenging open question in the foundation of the quantum theory. This book describes the problems, and the attempts and achievements in defining, formalizing and measuring different time quantities in quantum theory, such as the parametric (clock) time, tunneling times, decay times, dwell times, delay times, arrival times or jump times. This multi-authored book, written as an introductory guide for newcomers to the subject, as well as a useful source of information for the expert, covers many of the open questions. After the brief historical overview in the introduction, 12 contributions are devoted to conceptual and theoretical investigations as well as experimental issues in quantum-mechanical time measurements. This novel monograph should attract physicists as well as philosophers of science working in the foundations of quantum physics. For this revised second edition, all chapters have been updated and extended where appropriate. (orig.)

  16. An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.

    Science.gov (United States)

    Liu, Jian; Miller, William H

    2011-03-14

    We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

  17. Analogies between optical and quantum mechanical angular momentum.

    Science.gov (United States)

    Nienhuis, Gerard

    2017-02-28

    The insight that a beam of light can carry orbital angular momentum (AM) in its propagation direction came up in 1992 as a surprise. Nevertheless, the existence of momentum and AM of an electromagnetic field has been well known since the days of Maxwell. We compare the expressions for densities of AM in general three-dimensional modes and in paraxial modes. Despite their classical nature, these expressions have a suggestive quantum mechanical appearance, in terms of linear operators acting on mode functions. In addition, paraxial wave optics has several analogies with real quantum mechanics, both with the wave function of a free quantum particle and with a quantum harmonic oscillator. We discuss how these analogies can be applied.This article is part of the themed issue 'Optical orbital angular momentum'. © 2017 The Author(s).

  18. Quantum mechanics I the fundamentals

    CERN Document Server

    Rajasekar, S

    2015-01-01

    Quantum Mechanics I: The Fundamentals provides a graduate-level account of the behavior of matter and energy at the molecular, atomic, nuclear, and sub-nuclear levels. It covers basic concepts, mathematical formalism, and applications to physically important systems.

  19. Identifying mechanisms in the control of quantum dynamics through Hamiltonian encoding

    International Nuclear Information System (INIS)

    Mitra, Abhra; Rabitz, Herschel

    2003-01-01

    A variety of means are now available to design control fields for manipulating the evolution of quantum systems. However, the underlying physical mechanisms often remain obscure, especially in the cases of strong fields and high quantum state congestion. This paper proposes a method to quantitatively determine the various pathways taken by a quantum system in going from the initial state to the final target. The mechanism is revealed by encoding a signal in the system Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time-evolution operator. The relevant interfering pathways determined by this analysis give insight into the physical mechanisms operative during the evolution of the quantum system. A hierarchy of mechanism identification algorithms with increasing ability to extract more detailed pathway information is presented. The mechanism identification concept is presented in the context of analyzing computer simulations of controlled dynamics. As illustrations of the concept, mechanisms are identified in the control of several simple, discrete-state quantum systems. The mechanism analysis tools reveal the roles of multiple interacting quantum pathways to maximally take advantage of constructive and destructive interference. Similar procedures may be applied directly in the laboratory to identify control mechanisms without resort to computer modeling, although this extension is not addressed in this paper

  20. Comparison of quantum-mechanical and semiclassical approaches for an analysis of spin dynamics in quantum dots

    International Nuclear Information System (INIS)

    Petrov, M. Yu.; Yakovlev, S. V.

    2012-01-01

    Two approaches to the description of spin dynamics of electron-nuclear system in quantum dots are compared: the quantum-mechanical one is based on direct diagonalization of the model Hamiltonian and semiclassical one is based on coupled equations for precession of mean electron spin and mean spin of nuclear spin fluctuations. The comparison was done for a model problem describing periodic excitation of electron-nuclear system by optical excitation. The computation results show that scattering of parameters related to fluctuation of the nuclear spin system leads to appearance of an ordered state in the system caused by periodic excitation and to the effect of electron-spin mode locking in an external magnetic field. It is concluded that both models can qualitatively describe the mode-locking effect, however give significantly different quantitative results. This may indicate the limited applicability of the precession model for describing the spin dynamics in quantum dots in the presence of optical pumping.