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Sample records for relativistic quantum mechanics

  1. 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.)

  2. 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

  3. Relativistic quantum mechanics

    CERN Document Server

    Horwitz, Lawrence P

    2015-01-01

    This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. Th...

  4. 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.

  5. 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.

  6. 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

  7. Point form relativistic quantum mechanics and relativistic SU(6)

    Science.gov (United States)

    Klink, W. H.

    1993-01-01

    The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.

  8. 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...

  9. 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.

  10. 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.

  11. Time Operator in Relativistic Quantum Mechanics

    Science.gov (United States)

    Khorasani, Sina

    2017-07-01

    It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

  12. Relativistic quantum mechanics of bosons

    International Nuclear Information System (INIS)

    Ghose, P.; Home, D.; Sinha Roy, M.N.

    1993-01-01

    We show that it is possible to use the Klein-Gordon, Proca and Maxwell formulations to construct multi-component relativistic configuration space wavefunctions of spin-0 and spin-1 bosons in an external field. These wavefunctions satisfy the first-order Kemmer-Duffin equation. The crucial ingredient is the use of the future-causal normal n μ (n μ n μ =1, n 0 >0) to the space-like hypersurfaces foliating space-time, inherent in the concept of a relativistic wavefunction, to construct a conserved future-causal probability current four-vector from the second-rank energy-momentum tensor, following Holland's prescription. The existence of a Hermitian position operator, localized solutions, compatibility with the second quantized theories and the question of interpretation are discussed. (orig.)

  13. 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

  14. 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.

  15. Quadratic hamiltonians and relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

    1981-01-01

    For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

  16. Causal localizations in relativistic quantum mechanics

    Science.gov (United States)

    Castrigiano, Domenico P. L.; Leiseifer, Andreas D.

    2015-07-01

    Causal localizations describe the position of quantum systems moving not faster than light. They are constructed for the systems with finite spinor dimension. At the center of interest are the massive relativistic systems. For every positive mass, there is the sequence of Dirac tensor-localizations, which provides a complete set of inequivalent irreducible causal localizations. They obey the principle of special relativity and are fully Poincaré covariant. The boosters are determined by the causal position operator and the other Poincaré generators. The localization with minimal spinor dimension is the Dirac localization. Thus, the Dirac equation is derived here as a mere consequence of the principle of causality. Moreover, the higher tensor-localizations, not known so far, follow from Dirac's localization by a simple construction. The probability of localization for positive energy states results to be described by causal positive operator valued (PO-) localizations, which are the traces of the causal localizations on the subspaces of positive energy. These causal Poincaré covariant PO-localizations for every irreducible massive relativistic system were, all the more, not known before. They are shown to be separated. Hence, the positive energy systems can be localized within every open region by a suitable preparation as accurately as desired. Finally, the attempt is made to provide an interpretation of the PO-localization operators within the frame of conventional quantum mechanics attributing an important role to the negative energy states.

  17. Dirac's aether in relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Petroni, N.C.; Bari Univ.; Vigier, J.P.

    1984-01-01

    The paper concerns Dirac's aether model, based on a stochastic covariant distribution of subquantum motions. Stochastic derivation of the relativistic quantum equations; deterministic nonlocal interpretation of the Aspect-Rapisarda experiments on the EPR paradox; and photon interference with itself; are all discussed. (U.K.)

  18. 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

  19. Relativistic entanglement from relativistic quantum mechanics in the rest-frame instant form of dynamics

    International Nuclear Information System (INIS)

    Lusanna, Luca

    2011-01-01

    After a review of the problems induced by the Lorentz signature of Minkowski space-time, like the need of a clock synchronization convention for the definition of 3-space and the complexity of the notion of relativistic center of mass, there is the introduction of a new formulation of relativistic quantum mechanics compatible with the theory of relativistic bound states. In it the zeroth postulate of non-relativistic quantum mechanics is not valid and the physics is described in the rest frame by a Hilbert space containing only relative variables. The non-locality of the Poincare' generators imply a kinematical non-locality and non-separability influencing the theory of relativistic entanglement and not connected with the standard quantum non-locality.

  20. Lectures on relativistic quantum mechanics and path integration

    International Nuclear Information System (INIS)

    Gunn, J.M.F.

    1989-02-01

    The question posed is why bother with relativistic quantum mechanics? Three reasons are given: First that there are many experimental phenomena which cannot be explained in non-relativistic terms. Secondly it would be unsatisfactory if relativity and quantum mechanics could not be united. Thirdly, there are theoretical reasons why new effects can be expected at relativistic velocities. The objectives of the course are to set up relativistic analogues of the Schroedinger equation and to understand their consequences. In doing so there are some questions which are raised and discussed such as can a first order equation be used to describe spin 0 particles and a second order equation be used to describe spin 1/ 2 (author)

  1. Local U(2,2) Symmetry in Relativistic Quantum Mechanics

    OpenAIRE

    Finster, Felix

    1997-01-01

    Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory.

  2. Local U(2,2) symmetry in relativistic quantum mechanics

    Science.gov (United States)

    Finster, Felix

    1998-12-01

    Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory.

  3. Elements of non-relativistic quantum mechanics

    CERN Document Server

    Sobrino, Luis

    1996-01-01

    This book presents the basic structure of quantum mechanics, the elements needed to properly understand the subject and its applications. It is written at a level which is intermediate between the standard graduate textbooks, which it intends to supplement, and the more advanced mathematical writings in the subject. Particular attention is given to the concepts of kinematical and dynamical symmetries. The unifying thread that links the study of particles and systems of particles is the connection between Galilean invariance and the fundamental observables of a system. The mathematical appendic

  4. The Wigner function in the relativistic quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Kowalski, K., E-mail: kowalski@uni.lodz.pl; Rembieliński, J.

    2016-12-15

    A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation. - Highlights: • We study the Wigner function for a quantum spinless relativistic particle. • We discuss the relativistic Wigner function introduced by Zavialov and Malokostov. • We introduce relativistic Wigner function based on the standard definition. • We find analytic expressions for relativistic Wigner functions.

  5. 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.

  6. Spacetime alternatives in the quantum mechanics of a relativistic particle

    International Nuclear Information System (INIS)

    Whelan, J.T.

    1994-01-01

    Hartle's generalized quantum mechanics formalism is used to examine spacetime coarse grainings, i.e., sets of alternatives defined with respect to a region extended in time as well as space, in the quantum mechanics of a free relativistic particle. For a simple coarse graining and suitable initial conditions, tractable formulas are found for branch wave functions. Despite the nonlocality of the positive-definite version of the Klein-Gordon inner product, which means that nonoverlapping branches are not sufficient to imply decoherence, some initial conditions are found to give decoherence and allow the consistent assignment of probabilities

  7. Relativistic rotators: a quantum mechanical de Sitter bundle

    International Nuclear Information System (INIS)

    Boehm, A.

    1976-02-01

    If de Sitter fiber bundle over space time is the classical picture of hadrons then for a quantum mechanical description one has to generalize the concept of a principal fiber bundle to a bundle that contains the representation of the group of motion. This idea is related to the relativistic rotator model, and the radius of the de Sitter fiber is determined from the experimental hadron spectrum

  8. On the relativistic quantum mechanics of two interacting spinless particles

    International Nuclear Information System (INIS)

    Rizov, V.A.; Sazdjian, H.; Todorov, I.T.

    1984-05-01

    The L 2 -scalar product ∫ PHI*(x)PSI(x) d 3 x is not appropriate for the space of states describing the center-of-mass relative motion of two relativistic particles whose interaction is given by an energy dependent quasipotential. The problem already appears in the relativistic quantum mechanics of a Klein-Gordon charged particle in an external field. We extend the methods developed for that case to study a two-particle system with an energy independent scalar interaction as well as the relativistic Coulomb problem. We write down a Poincare invariant inner product for which the eigenfunctions corresponding to different energy eigenvalues are orthogonal. We also construct a perturbative expansion for bound-state energy eigenvalues corresponding to an arbitrary energy dependent (quasipotential) correction to an unperturbed Hamiltonian with a known spectrum. The description of observables and transition probabilities for eigenvalue problems with a polynomial dependence on the spectral parameter is also discussed

  9. 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

  10. 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

  11. Classical particle limit of non-relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Zucchini, R.

    1984-01-01

    We study the classical particle limit of non-relativistic quantum mechanics. We show that the unitary group describing the evolution of the quantum fluctuation around any classical phase orbit has a classical limit as h → 0 in the strong operator topology for a very large class of time independent scalar and vector potentials, which in practice covers all physically interesting cases. We also show that the mean values of the quantum mechanical position and velocity operators on suitable states, obtained by time evolution of the product of a Weyl operator centred around the large coordinates and momenta and a fixed n-independent wave function, converge to the solution of the classical equations with initial data as h → 0 for a broad class of repulsive interactions

  12. 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.

  13. A finite Zitterbewegung model for relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1990-01-01

    Starting from steps of length h/mc and time intervals h/mc 2 , which imply a quasi-local Zitterbewegung with velocity steps ±c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig

  14. A finite Zitterbewegung model for relativistic quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Noyes, H.P.

    1990-02-19

    Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.

  15. Relativistic-particle quantum mechanics (applications and approximations) II

    International Nuclear Information System (INIS)

    Coester, F.

    1981-01-01

    In this lecture I hope to show that relativistic-particle quantum mechanics with direct interactions is a useful tool for building models applicable to hadron systems at intermediate energies. To do this I will first describe a class of models designed to incorporate nucleon-nucleon interactions, pion production, absorption and scattering into a single dynamical framework without dressing the nucleons with pion clouds. The second major topic concerns electromagnetic interactions. In the previous lecture I specifically excluded long-rang forces and zero-mass particles. Since many of the experimental data in hadron physics involve electromagnetic interactions this limitation is a major defect which must be addressed

  16. Relativistic quantum mechanics and introduction to field theory

    Energy Technology Data Exchange (ETDEWEB)

    Yndurain, F.J. [Universidad Autonoma de Madrid (Spain). Dept. de Fisica Teorica

    1996-12-01

    The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources.

  17. Relativistic quantum mechanics and introduction to field theory

    International Nuclear Information System (INIS)

    Yndurain, F.J.

    1996-01-01

    The following topics were dealt with: relativistic transformations, the Lorentz group, Klein-Gordon equation, spinless particles, spin 1/2 particles, Dirac particle in a potential, massive spin 1 particles, massless spin 1 particles, relativistic collisions, S matrix, cross sections, decay rates, partial wave analysis, electromagnetic field quantization, interaction of radiation with matter, interactions in quantum field theory and relativistic interactions with classical sources

  18. Is there a relativistic nonlinear generalization of quantum mechanics?

    Energy Technology Data Exchange (ETDEWEB)

    Elze, Hans-Thomas [Dipartimento di Fisica ' Enrico Fermi' , Largo Pontecorvo 3, I-56127 Pisa (Italy)

    2007-05-15

    Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of a U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.

  19. Handbook of relativistic quantum chemistry

    International Nuclear Information System (INIS)

    Liu, Wenjian

    2017-01-01

    This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.

  20. Handbook of relativistic quantum chemistry

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Wenjian (ed.) [Peking Univ., Beijing (China). Center for Computational Science and Engineering

    2017-03-01

    This handbook focuses on the foundations of relativistic quantum mechanics and addresses a number of fundamental issues never covered before in a book. For instance: How can many-body theory be combined with quantum electrodynamics? How can quantum electrodynamics be interfaced with relativistic quantum chemistry? What is the most appropriate relativistic many-electron Hamiltonian? How can we achieve relativistic explicit correlation? How can we formulate relativistic properties? - just to name a few. Since relativistic quantum chemistry is an integral component of computational chemistry, this handbook also supplements the ''Handbook of Computational Chemistry''. Generally speaking, it aims to establish the 'big picture' of relativistic molecular quantum mechanics as the union of quantum electrodynamics and relativistic quantum chemistry. Accordingly, it provides an accessible introduction for readers new to the field, presents advanced methodologies for experts, and discusses possible future perspectives, helping readers understand when/how to apply/develop the methodologies.

  1. 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)

  2. Outline of a nonlinear, relativistic quantum mechanics of extended particles

    International Nuclear Information System (INIS)

    Mielke, E.W.

    1981-01-01

    A quantum theory of intrinsically extended particles similar to de Broglie's theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)

  3. Outline of a nonlinear, relativistic quantum mechanics of extended particles

    International Nuclear Information System (INIS)

    Mielke, E.W.

    1981-01-01

    A quantum theory of intrinsically extended particles similar to de Broglie's Theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)

  4. Structure and applications of point form relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Klink, W.H.

    2003-01-01

    The framework of point form relativistic quantum mechanics is used to construct mass and current operators for hadronic systems with finite degree of freedom. For the point form all of the interactions are in the four-momentum operator and, since Lorentz transformations are kinematic, the theory is manifestly covariant. In the Bakamjian-Thomas version of the point form the four-momentum operator is written as a product of the four-velocity operator and mass operator, where the mass operator is the sum of free and interacting mass operators. Interacting mass operators can be constructed from vertices, matrix elements of local field operators evaluated at the space-time point zero, where the states are eigenstates of the four-velocity. Applications include the study of the spectra and widths of vector mesons, viewed as bound states of quark-antiquark pairs. Besides mass operators, current operators are needed to compute form factors. Form factors are matrix elements of current operators on mass operator eigenstates and are often calculated with one-body current operators (in the point form this is called the point form spectator approximation); but in a properly relativistic theory there must also be many-body current operators. Minimal currents needed to satisfy current conservation in the presence of hadronic interactions (called dynamically determined currents) are shown to be easily calculated in the point form. (author)

  5. 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

  6. On some solvable models in non-relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Shabani, J.; Shayo, L.K.

    1985-11-01

    The theory of self-adjoint extensions is employed to generalize some previous results in non-relativistic quantum interactions. In particular, the Hamiltonian H=-Δ+V, where Δ is the Laplacian and the potential V consists of a strongly singular interaction, a Coulomb and a delta-shell interaction is studied. The spectral properties are discussed and phase shifts as well as low energy parameters are obtained. (author)

  7. 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

  8. Losing energy in classical, relativistic and quantum mechanics

    NARCIS (Netherlands)

    Atkinson, David

    A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. In relativistic mechanics, however,

  9. 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

  10. Axioms for quantum mechanics: relativistic causality, retrocausality, and the existence of a classical limit

    Science.gov (United States)

    Rohrlich, Daniel

    Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantum mechanics reconciles them. Can we indeed derive quantum mechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this limit, PR-box correlations violaterelativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantum mechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantum mechanics, it points to the Hilbert space structure that underlies quantum correlations. I thank the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (Grant No. 1190/13) for support.

  11. 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)

  12. Relativistic quantum logic

    International Nuclear Information System (INIS)

    Mittelstaedt, P.

    1983-01-01

    on the basis of the well-known quantum logic and quantum probability a formal language of relativistic quantum physics is developed. This language incorporates quantum logical as well as relativistic restrictions. It is shown that relativity imposes serious restrictions on the validity regions of propositions in space-time. By an additional postulate this relativistic quantum logic can be made consistent. The results of this paper are derived exclusively within the formal quantum language; they are, however, in accordance with well-known facts of relativistic quantum physics in Hilbert space. (author)

  13. Fiber bundles in non-relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Moylan, P.

    1979-11-01

    The problem of describing a quantum-mechanical system with symmetry by a fiber bundle is considered. The quantization of a fiber bundle is introduced. Fiber bundles for the Kepler problem and the rotator are constructed. The fiber bundle concept provides a new model for a physical system: it provides a model for an elementary particle with extension having integral values of spin. 5 figures

  14. Quantum mechanics in general relativity and its special - relativistic limit

    International Nuclear Information System (INIS)

    Tagirov, Eh.A.

    1998-01-01

    Quantum mechanics of a neutral point-like particle in the general Riemannian space-time is constructed starting with the general Fock representation of the quantum scalar field. The known ambiguity of the representation is removed by the requirement that the quasi-one-particle wave functions in configurational space should admit the Born probabilistic interpretation after a transformation, generally nonlocal, and therefore may be considered as the one-particle wave functions. Operators of momentum and spatial position of a particle acting in the space of these transformed wave functions are deduced consecutively from basic naturally defined operators of the observables in the Fock space. They coincide with the canonical ones only in the case of the infinite velocity of light. In particular, even in the Minkowski space-time and inertial frames of reference , the operators of curvilinear coordinates do not commute

  15. Multiple-event probability in general-relativistic quantum mechanics. II. A discrete model

    International Nuclear Information System (INIS)

    Mondragon, Mauricio; Perez, Alejandro; Rovelli, Carlo

    2007-01-01

    We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper [Phys. Rev. D 75, 084033 (2007)]. We consider a version of the model with unitary time evolution and a version without unitary time evolution

  16. Towards relativistic quantum geometry

    Energy Technology Data Exchange (ETDEWEB)

    Ridao, Luis Santiago [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)

    2015-12-17

    We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner–Nordström black-hole is studied.

  17. 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

  18. Is relativistic quantum mechanics compatible with special relativity?

    International Nuclear Information System (INIS)

    Lavenda, B.H.

    2001-01-01

    The transformation from a time-dependent random walk to quantum mechanics converts a modified Bessel function into an ordinary one together with a phase factor e iπ/2 for each time the electron flips both direction and handedness. Causality requires the argument to be greater than the order of the Bessel function. Assuming equal probabilities for jumps ±1, the normalized modified Bessel function of an imaginary argument is the solution of the finite difference differential Schroedinger equation whereas the same function of a real argument satisfies the diffusion equation. In the nonrelativistic limit, the stability condition of the difference scheme contains the mass whereas in the ultrarelativistic limit only the velocity of light appears. Particle waves in the nonrelativistic limit become elastic waves in the ultrarelativistic limit with a phase shift in the frequency and wave number of π/2. The ordinary Bessel function satisfies a second order recurrence relation which is a finite difference differential wave equation, using non-nearest neighbors, whose solutions are the chirality components of a free-particle in the zero fermion mass limit. Reintroducing the mass by a phase transformation transforms the wave equation into the Klein-Gordon equation but does not admit a solution in terms of ordinary Bessel functions. However, a sign change of the mass term permits a solution in terms of a modified Bessel function whose recurrence formulas produce all the results of special relativity. The Lorentz transformation maximizes the integral of the modified Bessel function and determines the paths of steepest descent in the classical limit. If the definitions of frequency and wave number in terms of the phase were used in special relativity, the condition that the frame be inertial would equate the superluminal phase velocity with the particle velocity in violation of causality. In order to get surfaces of constant phase to move at the group velocity, an integrating

  19. Relativistic Quantum Revivals

    International Nuclear Information System (INIS)

    Strange, P.

    2010-01-01

    Quantum revivals are now a well-known phenomena within nonrelativistic quantum theory. In this Letter we display the effects of relativity on revivals and quantum carpets. It is generally believed that revivals do not occur within a relativistic regime. Here we show that while this is generally true, it is possible, in principle, to set up wave packets with specific mathematical properties that do exhibit exact revivals within a fully relativistic theory.

  20. Non-Hermitian interaction representation and its use in relativistic quantum mechanics

    Czech Academy of Sciences Publication Activity Database

    Znojil, Miloslav

    2017-01-01

    Roč. 385, č. 10 (2017), s. 162-179 ISSN 0003-4916 R&D Projects: GA ČR GA16-22945S Institutional support: RVO:61389005 Keywords : unitary quantum systems * non-Hermitian version of Dirac's interaction picture * complete set of time-evolution equations * application in relativistic quantum mechanics * Klein-Gordon example with space-time-dependent mass Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.465, year: 2016

  1. Study of the equations of a particle in Non- Relativistic Quantum Mechanics

    International Nuclear Information System (INIS)

    Miltao, Milton Souza Ribeiro; Silva, Vanessa Santos Teles da

    2011-01-01

    Full text: The study of group theory is relevant to the treatment of physical problems, in which concepts of invariance and symmetry are important. In the field of Non-Relativistic Quantum Mechanics, we can do algebraic considerations taking into account the principles of symmetry, considering the framework of the study of Galileo transformations, which have characteristics of group. Therefore, we discuss the Stern-Gerlach experiment that had the historical importance of demonstrating that the electron has an intrinsic angular momentum. Through discussion of this experiment, we found that the spin appears in Non-Relativistic Quantum Mechanics as a feature of the algebraic structure underlying any physical theory represented by a group. From these studies, we have algebraic considerations for physical systems in non-relativistic domain, which are described by the Schroedinger and Pauli equations, describing the dynamics of particles of spin zero and 1/2 respectively, taking into account the structure of the transformations Galileo. Due to the operatorial, we represent Galileo's transformations by matrices by choosing an appropriate basis of space-time. Using these arrays, we saw group characteristics associated with these transformations, which we call the Galileo Group. We note the invariance of the Schroedinger and Pauli equations after these changes, as well as the physical state associated with it, which is represented by a radius vector in Hilbert space. (author)

  2. Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics

    Science.gov (United States)

    Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert

    1995-05-01

    The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.

  3. Angular analyses in relativistic quantum mechanics; Analyses angulaires en mecanique quantique relativiste

    Energy Technology Data Exchange (ETDEWEB)

    Moussa, P [Commissariat a l' Energie Atomique, 91 - Saclay (France). Centre d' Etudes Nucleaires

    1968-06-01

    This work describes the angular analysis of reactions between particles with spin in a fully relativistic fashion. One particle states are introduced, following Wigner's method, as representations of the inhomogeneous Lorentz group. In order to perform the angular analyses, the reduction of the product of two representations of the inhomogeneous Lorentz group is studied. Clebsch-Gordan coefficients are computed for the following couplings: l-s coupling, helicity coupling, multipolar coupling, and symmetric coupling for more than two particles. Massless and massive particles are handled simultaneously. On the way we construct spinorial amplitudes and free fields; we recall how to establish convergence theorems for angular expansions from analyticity hypothesis. Finally we substitute these hypotheses to the idea of 'potential radius', which gives at low energy the usual 'centrifugal barrier' factors. The presence of such factors had never been deduced from hypotheses compatible with relativistic invariance. (author) [French] On decrit un formalisme permettant de tenir compte de l'invariance relativiste, dans l'analyse angulaire des amplitudes de reaction entre particules de spin quelconque. Suivant Wigner, les etats a une particule sont introduits a l'aide des representations du groupe de Lorentz inhomogene. Pour effectuer les analyses angulaires, on etudie la reduction du produit de deux representations du groupe de Lorentz inhomogene. Les coefficients de Clebsch-Gordan correspondants sont calcules dans les couplages suivants: couplage l-s couplage d'helicite, couplage multipolaire, couplage symetrique pour plus de deux particules. Les particules de masse nulle et de masse non nulle sont traitees simultanement. Au passage, on introduit les amplitudes spinorielles et on construit les champs libres, on rappelle comment des hypotheses d'analyticite permettent d'etablir des theoremes de convergence pour les developpements angulaires. Enfin on fournit un substitut a la

  4. Comparison of different boost transformations for the calculation of form factors in relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Theussl, L.; Noguera, S.; Amghar, A.; Desplanques, B.

    2003-01-01

    The effect of different boost expressions, pertinent to the instant, front and point forms of relativistic quantum mechanics, is considered for the calculation of the ground-state form factor of a two-body system in simple scalar models. Results with a Galilean boost as well as an explicitly covariant calculation based on the Bethe-Salpeter approach are given for comparison. It is found that the present so-called point-form calculations of form factors strongly deviate from all the other ones. This suggests that the formalism which underlies them requires further elaboration. A proposition in this sense is made. (author)

  5. Relativistic quantum cryptography

    International Nuclear Information System (INIS)

    Molotkov, S. N.

    2011-01-01

    A new protocol of quantum key distribution is proposed to transmit keys through free space. Along with quantum-mechanical restrictions on the discernibility of nonorthogonal quantum states, the protocol uses additional restrictions imposed by special relativity theory. Unlike all existing quantum key distribution protocols, this protocol ensures key secrecy for a not strictly one-photon source of quantum states and an arbitrary length of a quantum communication channel.

  6. Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

    Science.gov (United States)

    Dvoeglazov, V. V.

    Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.

  7. Unifying quanta and relativity. Schroedinger`s attitude to relativistic quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Kragh, H. [Roskilde Universitetscenter (Denmark)

    1992-12-31

    A considerable part of Schroedinger`s scientific work focused on the relationship between quantum theory and the theory of relativity. This paper provides a historical analysis of his occupation on this subject in the period 1925-1934. The first section surveys the role played by relativity in Schroedinger`s formation of wave mechanics in 1925-1926; the second section analyzes his attempt to make sense of Dirac`s theory of the electron by proposing a relativistic wave equation with positive energies only. In this work, which took place in 1930-1931, Schroedinger discovered the Zitterbewegung that Dirac electrons will exhibit even in a field-free case. Schroedinger`s failed attempt to introduce an alternative to the Dirac theory was part of his general dissatisfaction with the current state of quantum mechanics. It is argued that, to a large extent, his work on the Dirac theory was philosophically motivated and that it contributed to his alienation from mainstream quantum physics in the 1930s. (author). 54 refs.

  8. Relativistic wave mechanics

    CERN Document Server

    Corinaldesi, Ernesto

    1963-01-01

    Geared toward advanced undergraduate and graduate students of physics, this text provides readers with a background in relativistic wave mechanics and prepares them for the study of field theory. The treatment originated as a series of lectures from a course on advanced quantum mechanics that has been further amplified by student contributions.An introductory section related to particles and wave functions precedes the three-part treatment. An examination of particles of spin zero follows, addressing wave equation, Lagrangian formalism, physical quantities as mean values, translation and rotat

  9. Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

    International Nuclear Information System (INIS)

    Donker, H.C.; Katsnelson, M.I.; De Raedt, H.; Michielsen, K.

    2016-01-01

    The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds. - Highlights: • Logical inference applied to relativistic, massive, charged, and spinless particle experiments leads to the Klein–Gordon equation. • The relativistic Hamilton–Jacobi is scrutinized by employing a field description for the four-velocity. • Logical inference allows analysis of experiments with uncertainty in detection events and experimental conditions.

  10. Five-dimensional Hamiltonian-Jacobi approach to relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Rose, Harald

    2003-01-01

    A novel theory is outlined for describing the dynamics of relativistic electrons and positrons. By introducing the Lorentz-invariant universal time as a fifth independent variable, the Hamilton-Jacobi formalism of classical mechanics is extended from three to four spatial dimensions. This approach allows one to incorporate gravitation and spin interactions in the extended five-dimensional Lagrangian in a covariant form. The universal time has the function of a hidden Bell parameter. By employing the method of variation with respect to the four coordinates of the particle and the components of the electromagnetic field, the path equation and the electromagnetic field produced by the charge and the spin of the moving particle are derived. In addition the covariant equations for the dynamics of the components of the spin tensor are obtained. These equations can be transformed to the familiar BMT equation in the case of homogeneous electromagnetic fields. The quantization of the five-dimensional Hamilton-Jacobi equation yields a five-dimensional spinor wave equation, which degenerates to the Dirac equation in the stationary case if we neglect gravitation. The quantity which corresponds to the probability density of standard quantum mechanics is the four-dimensional mass density which has a real physical meaning. By means of the Green method the wave equation is transformed into an integral equation enabling a covariant relativistic path integral formulation. Using this approach a very accurate approximation for the four-dimensional propagator is derived. The proposed formalism makes Dirac's hole theory obsolete and can readily be extended to many particles

  11. Quantum mechanics of relativistic particles in multiply connected spaces and the Aharonov-Bohm effect

    International Nuclear Information System (INIS)

    Gamboa, J.; Rivelles, V.O.

    1990-04-01

    We consider the motion of free relativistic particles in multiply connected spaces. We show that if one of the spatial dimensions has the topology of a circle then the D dimensional spacetime is compactified to D-1 dimensions and the particle mass increases by an amount which is proportional to a quantum phase factor and inversely proportional to the radius of the circle. We also consider the relativistic Aharonov-Bohm effect and we show that the interference pattern is a universal characteristic due only to the topological properties of the experimental situation and not to the intrinsic properties of the particle. The propagators are calculated in both situations. (author) [pt

  12. Relativistic implications of the quantum phase

    International Nuclear Information System (INIS)

    Low, Stephen G

    2012-01-01

    The quantum phase leads to projective representations of symmetry groups in quantum mechanics. The projective representations are equivalent to the unitary representations of the central extension of the group. A celebrated example is Wigner's formulation of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group. However, Wigner's formulation makes no mention of the Weyl-Heisenberg group and the hermitian representation of its algebra that are the Heisenberg commutation relations fundamental to quantum physics. We put aside the relativistic symmetry and show that the maximal quantum symmetry that leaves the Heisenberg commutation relations invariant is the projective representations of the conformally scaled inhomogeneous symplectic group. The Weyl-Heisenberg group and noncommutative structure arises directly because the quantum phase requires projective representations. We then consider the relativistic implications of the quantum phase that lead to the Born line element and the projective representations of an inhomogeneous unitary group that defines a noninertial quantum theory. (Understanding noninertial quantum mechanics is a prelude to understanding quantum gravity.) The remarkable properties of this symmetry and its limits are studied.

  13. Consistent resolution of some relativistic quantum paradoxes

    International Nuclear Information System (INIS)

    Griffiths, Robert B.

    2002-01-01

    A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics

  14. Relativistic viscoelastic fluid mechanics

    International Nuclear Information System (INIS)

    Fukuma, Masafumi; Sakatani, Yuho

    2011-01-01

    A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

  15. Relativistic viscoelastic fluid mechanics.

    Science.gov (United States)

    Fukuma, Masafumi; Sakatani, Yuho

    2011-08-01

    A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

  16. Quantum gates via relativistic remote control

    Energy Technology Data Exchange (ETDEWEB)

    Martín-Martínez, Eduardo, E-mail: emartinm@uwaterloo.ca [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Dept. Applied Math., University of Waterloo, Ontario, N2L 3G1 (Canada); Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5 (Canada); Sutherland, Chris [Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada)

    2014-12-12

    We harness relativistic effects to gain quantum control on a stationary qubit in an optical cavity by controlling the non-inertial motion of a different probe atom. Furthermore, we show that by considering relativistic trajectories of the probe, we enhance the efficiency of the quantum control. We explore the possible use of these relativistic techniques to build 1-qubit quantum gates.

  17. 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.

  18. Localization and Entanglement in Relativistic Quantum Physics

    Science.gov (United States)

    Yngvason, Jakob

    These notes are a slightly expanded version of a lecture presented in February 2012 at the workshop "The Message of Quantum Science—Attempts Towards a Synthesis" held at the ZIF in Bielefeld. The participants were physicists with a wide range of different expertise and interests. The lecture was intended as a survey of a small selection of the insights into the structure of relativistic quantum physics that have accumulated through the efforts of many people over more than 50 years. (Including, among many others, R. Haag, H. Araki, D. Kastler, H.-J. Borchers, A. Wightman, R. Streater, B. Schroer, H. Reeh, S. Schlieder, S. Doplicher, J. Roberts, R. Jost, K. Hepp, J. Fröhlich, J. Glimm, A. Jaffe, J. Bisognano, E. Wichmann, D. Buchholz, K. Fredenhagen, R. Longo, D. Guido, R. Brunetti, J. Mund, S. Summers, R. Werner, H. Narnhofer, R. Verch, G. Lechner, ….) This contribution discusses some facts about relativistic quantum physics, most of which are quite familiar to practitioners of Algebraic Quantum Field Theory (AQFT) [Also known as Local Quantum Physics (Haag, Local quantum physics. Springer, Berlin, 1992).] but less well known outside this community. No claim of originality is made; the goal of this contribution is merely to present these facts in a simple and concise manner, focusing on the following issues: Explaining how quantum mechanics (QM) combined with (special) relativity, in particular an upper bound on the propagation velocity of effects, leads naturally to systems with an infinite number of degrees of freedom (relativistic quantum fields).

  19. Relativistic quantum chemistry on quantum computers

    DEFF Research Database (Denmark)

    Veis, L.; Visnak, J.; Fleig, T.

    2012-01-01

    The past few years have witnessed a remarkable interest in the application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, proof-of-principle experimental realizations have been reported. However, so far only...... the nonrelativistic regime (i.e., the Schrodinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. We present a quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem of the Dirac......-Coulomb Hamiltonian on a quantum computer and demonstrate the functionality of the proposed procedure by numerical simulations of computations of the spin-orbit splitting in the SbH molecule. Finally, we propose quantum circuits with three qubits and nine or ten controlled-NOT (CNOT) gates, which implement a proof...

  20. What is the uncertainty principle of non-relativistic quantum mechanics?

    Science.gov (United States)

    Riggs, Peter J.

    2018-05-01

    After more than ninety years of discussions over the uncertainty principle, there is still no universal agreement on what the principle states. The Robertson uncertainty relation (incorporating standard deviations) is given as the mathematical expression of the principle in most quantum mechanics textbooks. However, the uncertainty principle is not merely a statement of what any of the several uncertainty relations affirm. It is suggested that a better approach would be to present the uncertainty principle as a statement about the probability distributions of incompatible variables and the resulting restrictions on quantum states.

  1. Relativistic quantum chaos-An emergent interdisciplinary field.

    Science.gov (United States)

    Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

    2018-05-01

    Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

  2. Relativistic quantum chaos—An emergent interdisciplinary field

    Science.gov (United States)

    Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

    2018-05-01

    Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics—all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

  3. Relativistic quantum cryptography

    Science.gov (United States)

    Kaniewski, Jedrzej

    Special relativity states that information cannot travel faster than the speed of light, which means that communication between agents occupying distinct locations incurs some minimal delay. Alternatively, we can see it as temporary communication constraints between distinct agents and such constraints turn out to be useful for cryptographic purposes. In relativistic cryptography we consider protocols in which interactions occur at distinct locations at well-defined times and we investigate why such a setting allows to implement primitives which would not be possible otherwise. (Abstract shortened by UMI.).

  4. Relativistic quantum cryptography

    International Nuclear Information System (INIS)

    Radchenko, I V; Kravtsov, K S; Kulik, S P; Molotkov, S N

    2014-01-01

    Quantum key distribution (QKD) is a concept of secret key exchange supported by fundamentals of quantum physics. Its perfect realization offers unconditional key security, however, known practical schemes are potentially vulnerable if the quantum channel loss exceeds a certain realization-specific bound. This discrepancy is caused by the fact that any practical photon source has a non-zero probability of emitting two or more photons at a time, while theory needs exactly one. We report an essentially different QKD scheme based on both quantum physics and theory of relativity. It works flawlessly with practical photon sources at arbitrary large channel loss. Our scheme is naturally tailored for free-space optical channels, and may be used in ground-to-satellite communications, where losses are prohibitively large and unpredictable for conventional QKD. (letters)

  5. Some consequences of the Fourier analysis on the Lorentz group for relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Mavrodiev, S.Ch.

    1974-01-01

    On the basis of the analogy between the nonrelativistic and relativistic Fourier analysis the uncertainty relation for rapidity and relativistic relative coordinate is formaly derived. A geometricla interpretation of the behaviour of the elastic scattering differential cross section is given too

  6. Blue functions: probability and current density propagators in non-relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Withers, L P Jr

    2011-01-01

    Like a Green function to propagate a particle's wavefunction in time, a Blue function is introduced to propagate the particle's probability and current density. Accordingly, the complete Blue function has four components. They are constructed from path integrals involving a quantity like the action that we call the motion. The Blue function acts on the displaced probability density as the kernel of an integral operator. As a result, we find that the Wigner density occurs as an expression for physical propagation. We also show that, in quantum mechanics, the displaced current density is conserved bilocally (in two places at one time), as expressed by a generalized continuity equation. (paper)

  7. Relativistic Quantum Transport in Graphene Systems

    Science.gov (United States)

    2015-07-09

    dimensional Dirac material systems. 2 List of Publications 1. X. Ni, L. Huang, Y.-C. Lai, and L. M. Pecora, “Effect of chaos on relativistic quantum...development of relativistic quantum devices based on graphene or alternative two-dimensional Dirac material systems. In the project period, we studied

  8. Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

    International Nuclear Information System (INIS)

    Zhang Fulin; Song Ci; Chen Jingling

    2009-01-01

    The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials has been proved commuting with the deformed orbital angular momentum L. When the potential takes the Coulomb form, the system has an SO(3) symmetry, and similarly the harmonic oscillator potential possesses an SU(2) symmetry. The generators of the symmetric groups are derived for these two systems separately. The corresponding energy spectra are yielded naturally from the Casimir operators. Their non-relativistic limits are also discussed

  9. 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...

  10. Quantum mechanics

    International Nuclear Information System (INIS)

    Ghatak, A.K.; Lokanathan, S.

    1975-01-01

    This textbook on quantum mechanics is intended for students at the graduate and post-graduate level. A balanced account of theory and applications is presented. Emphasis is laid on making results plausible and methods to be followed in solving problems. The various chapters in the book are devoted to the following: (1) Wave particle duality and uncertainty principle (2) Wave packets and time-dependent Schroedinger equation (3) Simple solutions of Schroedinger equation (4) Vector spaces and linear operators : Dirac notation (5) Angular momentum and spin (6) Addition of angular momenta (7) Time independent perturbation theory (8) The variational method (9) The WKB approximation (10) Elementary theory of scattering (11) Time-dependent perturbation theory (12) Motion in a magnetic field (13) Interaction of radiation with matter and (14) Relativistic theory. (A.K.)

  11. Relativistic extension of the Kay-Moses method for constructing transparent potentials in quantum mechanics

    International Nuclear Information System (INIS)

    Toyama, F.M.; Nogami, Y.; Zhao, Z.

    1993-01-01

    For the Dirac equation in one space dimension with a potential of the Lorentz scalar type, we present a complete solution for the problem of constructing a transparent potential. This is a relativistic extension of the Kay-Moses method which was developed for the nonrelativistic Schroedinger equation. There is an infinite family of transparent potentials. The potentials are all related to solutions of a class of coupled, nonlinear Dirac equations. In addition, it is argued that an admixture of a Lorentz vector component in the potential impairs perfect transparency

  12. 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

  13. Quantum theoretical physics is statistical and relativistic

    International Nuclear Information System (INIS)

    Harding, C.

    1980-01-01

    A new theoretical framework for the quantum mechanism is presented. It is based on a strict deterministic behavior of single systems. The conventional QM equation, however, is found to describe statistical results of many classical systems. It will be seen, moreover, that a rigorous synthesis of our theory requires relativistic kinematics. So, QM is not only a classical statistical theory, it is, of necessity, a relativistic theory. The equation of the theory does not just duplicate QM, it indicates an inherent nonlinearity in QM which is subject to experimental verification. It is shown, therefore, that conventional QM is a corollary of classical deterministic principles. It is suggested that this concept of nature conflicts with that prevalent in modern physics. (author)

  14. 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.)

  15. Insight into the Extraction Mechanism of Americium(III) over Europium(III) with Pyridylpyrazole: A Relativistic Quantum Chemistry Study.

    Science.gov (United States)

    Kong, Xiang-He; Wu, Qun-Yan; Wang, Cong-Zhi; Lan, Jian-Hui; Chai, Zhi-Fang; Nie, Chang-Ming; Shi, Wei-Qun

    2018-05-10

    Separation of trivalent actinides (An(III)) and lanthanides (Ln(III)) is one of the most important steps in spent nuclear fuel reprocessing. However, it is very difficult and challenging to separate them due to their similar chemical properties. Recently the pyridylpyrazole ligand (PypzH) has been identified to show good separation ability toward Am(III) over Eu(III). In this work, to explore the Am(III)/Eu(III) separation mechanism of PypzH at the molecular level, the geometrical structures, bonding nature, and thermodynamic behaviors of the Am(III) and Eu(III) complexes with PypzH ligands modified by alkyl chains (Cn-PypzH, n = 2, 4, 8) have been systematically investigated using scalar relativistic density functional theory (DFT). According to the NBO (natural bonding orbital) and QTAIM (quantum theory of atoms in molecules) analyses, the M-N bonds exhibit a certain degree of covalent character, and more covalency appears in Am-N bonds compared to Eu-N bonds. Thermodynamic analyses suggest that the 1:1 extraction reaction, [M(NO 3 )(H 2 O) 6 ] 2+ + PypzH + 2NO 3 - → M(PypzH)(NO 3 ) 3 (H 2 O) + 5H 2 O, is the most suitable for Am(III)/Eu(III) separation. Furthermore, the extraction ability and the Am(III)/Eu(III) selectivity of the ligand PypzH is indeed enhanced by adding alkyl-substituted chains in agreement with experimental observations. Besides this, the nitrogen atom of pyrazole ring plays a more significant role in the extraction reactions related to Am(III)/Eu(III) separation compared to that of pyridine ring. This work could identify the mechanism of the Am(III)/Eu(III) selectivity of the ligand PypzH and provide valuable theoretical information for achieving an efficient Am(III)/Eu(III) separation process for spent nuclear fuel reprocessing.

  16. Relativistic nuclear physics and quantum chromodynamics. Abstracts

    International Nuclear Information System (INIS)

    1994-01-01

    The data of investigations on problems of high energy physics are given. Special attention pays to quantum chromodynamics at large distances, cumulative processes, multiquark states and relativistic nuclear collisions

  17. 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.

  18. Relativistic non-Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2010-01-01

    Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u μ u μ + c 2 = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.

  19. 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...

  20. Relativistic quantum mechanic calculation of photoionization cross-section of hydrogenic and non-hydrogenic states using analytical potentials

    International Nuclear Information System (INIS)

    Rodriguez, R.; Gil, J.M.; Rubiano, J.G.; Florido, R.; Martel, P.; Minguez, E.

    2005-01-01

    Photoionization process is a subject of special importance in many areas of physics. Numerical methods must be used in order to obtain photoionization cross-sections for non-hydrogenic levels. The atomic data required to calculate them is huge so self-consistent calculations increase computing time considerably. Analytical potentials are a useful alternative because they avoid the iterative procedures typical in self-consistent models. In this work, we present a relativistic quantum calculation of photoionization cross-sections for isolated ions based on an analytical potential to obtain the required atomic data, which is valid both for hydrogenic and non-hydrogenic ions. Comparisons between our results and others obtained using either widely used analytical expressions for the cross-sections or more sophisticated calculations are done

  1. Observer dependence of quantum states in relativistic quantum field theories

    International Nuclear Information System (INIS)

    Malin, S.

    1982-01-01

    Quantum states can be understood as either (i) describing quantum systems or (ii) representing observers' knowledge about quantum systems. These different meanings are shown to imply different transformation properties in relativistic field theories. The rules for the reduction of quantum states and the transformation properties of quantum states under Lorentz transformations are derived for case (ii). The results obtained are applied to a quantum system recently presented and analyzed by Aharonov and Albert. It is shown that the present results, combined with Aharonov and Albert's, amount to a proof of Bohr's view that quantum states represent observers' knowledge about quantum systems

  2. Scattering in relativistic particle mechanics

    International Nuclear Information System (INIS)

    De Bievre, S.

    1986-01-01

    The problem of direct interaction in relativistic particle mechanics has been extensively studied and a variety of models has been proposed avoiding the conclusions of the so-called no-interaction theorems. In this thesis the authors studied scattering in the relativistic two-body problem. He uses the results to analyze gauge invariance in Hamiltonian constraint models and the uniqueness of the symplectic structure in manifestly covariant relativistic particle mechanics. A general geometric framework that underlies approaches to relativistic particle mechanics is presented and the kinematic properties of the scattering transformation, i.e., those properties that arise solely from the invariance of the theory under the Poincare group are studied. The second part of the analysis of the relativistic two-body scattering problem is devoted to the dynamical properties of the scattering process. Using general geometric arguments, gauge invariance of the scattering transformation in the Todorov-Komar Hamiltonian constraint model is proved. Finally, quantization of the models is discussed

  3. Frontiers in relativistic celestial mechanics

    CERN Document Server

    2014-01-01

    Relativistic celestial mechanics – investigating the motion celestial bodies under the influence of general relativity – is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics – starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area.

  4. Characterization of particle states in relativistic classical quantum theory

    International Nuclear Information System (INIS)

    Horwitz, L.P.; Rabin, Y.

    1977-02-01

    Classical and quantum relativistic mechanics are studied. The notion of a ''particle'' is defined in the classical case and the interpretation of mechanics in space-time is clarified. These notions are carried over to the quantum theory, as much as possible. The relation between the results of Feyman's path integral approach and the theory of Horwitz and Piron is discussed. The ''particle'' interpretation is shown to imply an asymptotic condition for scattering. A general method of constructing the dynamical mass spectrum of composite ''particle'' states is discussed. An interference experiment is proposed to affirm the interpretation and applicability of Stueckelberg type wave functions for actual physical phenomena. Some discussion of the relation of this relativistic quantum theory to Feynman's approach to quantum field theory is also given

  5. Relativistic predictive quantum potential: the N-body case

    International Nuclear Information System (INIS)

    Garuccio, A.; Kyprianidis, A.; Vigier, J.P.

    1984-01-01

    It is generalized to a system of N scalar particles the casual description with action at a distance already given for two-particle systems in EPR type of experiments. The many body quantum potential is shown to satisfy the predictivity constraints established by Droz-Vincent for relativistic mechanics

  6. Relativistic quantum metrology: exploiting relativity to improve quantum measurement technologies.

    Science.gov (United States)

    Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette

    2014-05-22

    We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.

  7. 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...

  8. 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.)

  9. 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

  10. 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.)

  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. 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.

  13. Relativistic classical limit of quantum theory

    International Nuclear Information System (INIS)

    Shin, G.R.; Rafelski, J.

    1993-01-01

    We study the classical limit of the equal-time relativistic quantum transport theory. We discuss in qualitative terms the need to fold first the Wigner function with a coarse-graining function. Only then does the singularity at ℎ→0 seem to be manageable. In the limit ℎ→0, we obtain the relativistic Vlasov equations for the particle and the antiparticle sector of the Fock space. Similarly, we address the evolution equations of the spin and the magnetic-moment density

  14. On the definition of the time evolution operator for time-independent Hamiltonians in non-relativistic quantum mechanics

    Science.gov (United States)

    Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.

    2017-09-01

    The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.

  15. Relativistic mechanics with reduced fields

    International Nuclear Information System (INIS)

    Sokolov, S.N.

    1996-01-01

    A new relativistic classical mechanics of interacting particles using a concept of a reduced field (RF) os proposed. RF is a mediator of interactions, the state of which is described by a finite number of two-argument functions. Ten of these functions correspond to the generators of the Poincare group. Equations of motion contain the retardation of interactions required by the causality principle and have form of a finite system of ordinary hereditary differential equations [ru

  16. Dirac particle in a box, and relativistic quantum Zeno dynamics

    International Nuclear Information System (INIS)

    Menon, Govind; Belyi, Sergey

    2004-01-01

    After developing a complete set of eigenfunctions for a Dirac particle restricted to a box, the quantum Zeno dynamics of a relativistic system is considered. The evolution of a continuously observed quantum mechanical system is governed by the theorem put forth by Misra and Sudarshan. One of the conditions for quantum Zeno dynamics to be manifest is that the Hamiltonian is semi-bounded. This Letter analyzes the effects of continuous observation of a particle whose time evolution is generated by the Dirac Hamiltonian. The theorem by Misra and Sudarshan is not applicable here since the Dirac operator is not semi-bounded

  17. Two point function for a simple general relativistic quantum model

    OpenAIRE

    Colosi, Daniele

    2007-01-01

    We study the quantum theory of a simple general relativistic quantum model of two coupled harmonic oscillators and compute the two-point function following a proposal first introduced in the context of loop quantum gravity.

  18. 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

  19. On the Velocity of Moving Relativistic Unstable Quantum Systems

    Directory of Open Access Journals (Sweden)

    K. Urbanowski

    2015-01-01

    Full Text Available We study properties of moving relativistic quantum unstable systems. We show that in contrast to the properties of classical particles and quantum stable objects the velocity of freely moving relativistic quantum unstable systems cannot be constant in time. We show that this new quantum effect results from the fundamental principles of the quantum theory and physics: it is a consequence of the principle of conservation of energy and of the fact that the mass of the quantum unstable system is not defined. This effect can affect the form of the decay law of moving relativistic quantum unstable systems.

  20. Classification of quantum relativistic orientable objects

    International Nuclear Information System (INIS)

    Gitman, D M; Shelepin, A L

    2011-01-01

    Extending our previous work 'Fields on the Poincare group and quantum description of orientable objects' (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

  1. 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.

  2. 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)

  3. 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.

  4. 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.

  5. 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.

  6. 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).

  7. 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

  8. Relativistic quantum similarities in atoms in position and momentum spaces

    International Nuclear Information System (INIS)

    Maldonado, P.; Sarsa, A.; Buendia, E.; Galvez, F.J.

    2011-01-01

    A study of different quantum similarity measures and their corresponding quantum similarity indices is carried out for the atoms from H to Lr (Z=1-103). Relativistic effects in both position and momentum spaces have been studied by comparing the relativistic values to the non-relativistic ones. We have used the atomic electron density in both position and momentum spaces obtained within relativistic and non-relativistic numerical-parameterized optimized effective potential approximations. -- Highlights: → Quantum similarity measures and indices in electronic structure of atoms. → Position and momentum electronic densities. → Similarity of relativistic and non-relativistic densities. → Similarity of core and valence regions of different atoms. → Dependence with Z along the Periodic Table.

  9. 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.

  10. A relativistic theory for continuous measurement of quantum fields

    International Nuclear Information System (INIS)

    Diosi, L.

    1990-04-01

    A formal theory for the continuous measurement of relativistic quantum fields is proposed. The corresponding scattering equations were derived. The proposed formalism reduces to known equations in the Markovian case. Two recent models for spontaneous quantum state reduction have been recovered in the framework of this theory. A possible example of the relativistic continuous measurement has been outlined in standard Quantum Electrodynamics. The continuous measurement theory possesses an alternative formulation in terms of interacting quantum and stochastic fields. (author) 23 refs

  11. Relativistic mechanics of two interacting particles and bilocal theory

    International Nuclear Information System (INIS)

    Takabayasi, Takehiko

    1975-01-01

    New relativistic mechanics of two-particle system is set forth, where the two constituent particles are interacting by an arbitrary (central) action-at-a-distance. The fundamental equations are presented in a form covariant under general transformation of parameters parametrizing the world lines of constituent particles. The theory represents the proper relativistic generalization of the usual Newtonian mechanics in the sense that it tends in the non-relativistic (and weak interaction) limit to the usual mechanics of two particles moving under a corresponding non-relativistic potential. For the analysis of theory it is convenient to choose a certain particular gauge (i.e., parametrization) fixed by two gauge relations. This brings the theory to a canonical formalism accompanied by two weak equations, and in this gauge quantization can be performed. The result verifies that the relativistic quantum mechanics for two particles interacting by an action-at-a-distance is just represented by a bilocal wave equation and a subsidiary condition, with the clarification of its correspondence-theoretical foundation and internal dynamics. As an example the case of Hooke-type force is illustrated, where the internal motions are elliptic oscillations in the center-of-mass frame. Its quantum theory just reproduces the original form of bilocal theory giving bound states lying on a straightly rising trajectory and on its daughter trajectories. (auth.)

  12. Classification of quantum relativistic orientable objects

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D M [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970, Sao Paulo, SP (Brazil); Shelepin, A L, E-mail: gitman@dfn.if.usp.br, E-mail: alex@shelepin.msk.ru [Moscow Institute of Radio Engineering, Electronics and Automation, Prospect Vernadskogo, 78, 117454 Moscow (Russian Federation)

    2011-01-15

    Extending our previous work 'Fields on the Poincare group and quantum description of orientable objects' (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3+1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

  13. 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

  14. Relativistic mechanics, time and inertia

    International Nuclear Information System (INIS)

    Kilmister, C.W.; Tocaci, E.

    1985-01-01

    This book offers a thought-provoking approach to the fundamentals of relativity, and is structured to provide a clear-cut introduction to the essentials of relativistic mechanics. It seeks to emphasize the sensible content of concepts, to improve on their inherent or often forgotten fuzziness, and to explore prospects for their further exploitation. The work also provides an analysis conducive to a rigorous, normative definition of Time, which is seen as a synthesis of universal motion, instrumental in defining a general measure to transformations, and as a sufficient reason to suppose that the speed of light must be the same in all inertial reference frames - hence showing this cardinal postulate to be a demonstrable truth. Moreover it provides an augmented perception of what inertial vs. non-inertial systems are. In addition, the book offers a natural, time-like interpretation of Space that departs from the usual converse approach; it offers a self-consistent proposal to rationalize the axiomatic grounds of mechanics, based on a single postulate in conjunction with the overall approach developed. (author). refs.; figs.; tabs

  15. Relativistic quantum chemistry the fundamental theory of molecular science

    CERN Document Server

    Reiher, Markus

    2014-01-01

    Einstein proposed his theory of special relativity in 1905. For a long time it was believed that this theory has no significant impact on chemistry. This view changed in the 1970s when it was realized that (nonrelativistic) Schrödinger quantum mechanics yields results on molecular properties that depart significantly from experimental results. Especially when heavy elements are involved, these quantitative deviations can be so large that qualitative chemical reasoning and understanding is affected. For this to grasp the appropriate many-electron theory has rapidly evolved. Nowadays relativist

  16. A quantum relativistic integrable model as the continuous limit of the six-vertex model

    International Nuclear Information System (INIS)

    Zhou, Y.K.

    1992-01-01

    The six-vertex model in two-dimensional statistical mechanics is used to construct the L-matrix of a one-dimensional quantum relativistic integrable model through a continuous limit. This is the first step to extend the method used earlier by the author to construct quantum completely integrable systems from other well-known two-dimensional vertex models. (orig.)

  17. Quantum ion-acoustic solitary waves in weak relativistic plasma

    Indian Academy of Sciences (India)

    Abstract. Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized two- species relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive ...

  18. 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

  19. 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...

  20. Coordinates in relativistic Hamiltonian mechanics

    International Nuclear Information System (INIS)

    Sokolov, S.N.

    1984-01-01

    The physical (covariant and measurable) coordinates of free particles and covariant coordinates of the center of inertia are found for three main forms of relativistic dynamics. In the point form of dynamics, the covariant coordinates of two directly interacting particles are found, and the equations of motion are brought to the explicitly covariant form. These equations are generalized to the case of interaction with an external electromagnetic field

  1. 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)

  2. Relativistic quantum theory of composite systems

    International Nuclear Information System (INIS)

    Sogami, I.

    1978-01-01

    A relativistic quantum theory free from the difficulties of tachyons and ghosts is formulated to describe the scattering processes between composite systems of spinless quarks. To evade the complication brewed by introducing gluon fields or strings, valence quarks are effectively assumed to be in the relative motion of harmonic oscillation correlating with the motion of the composite system as a whole. A quark-antiquark system is represented by a bilocal field describing a sequence of mesons and every meson is identified with the composite system in a definite eigenstate of relative motion. The quantization is performed in the interaction picture, so that the microcausal condition is satisfied by local fields which result from the decomposition of bilocal fields. Imposing a weakened macrocausal condition on the whole motion of the extended system, a causal bilocal propagator is defined and a consistent time ordering among bilocal fields is defined. The invariant S-matrix is obtained and the graphical method for the calculation of its elements is developed in parallel with the conventional local field theory. For the (bilocal field) 3 interaction any malignant divergence does not appear excepting those in the renormalizable local field theory. The theory provides one promising and comprehensive phenomenology of hadrons which is suitable especially to describe the hard structure of hadrons. (author)

  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. Analysis of the EPR-experiment by relativistic quantum logic

    International Nuclear Information System (INIS)

    Mittelstaedt, P.

    1984-01-01

    The Einstein-Podolsky-Rosen-experiment is analysed in the framework of an abstract language for relativistic quantum physics, which can be founded on the most general possibilities of physical observations and without any recourse to the Hilbert-space formulation of relativistic quantum theory. -Within this approach one obtains nonlocal correlations between the two EPR-systems in accordance with recent experiments and with quantum theory. These correlations can, however, not be used in order to produce superluminal signals and thus to violate Einstein-causality and special relativity. (author)

  5. 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.

  6. 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)

  7. Relativistic Celestial Mechanics of the Solar System

    CERN Document Server

    Kopeikin, Sergei; Kaplan, George

    2011-01-01

    This authoritative book presents the theoretical development of gravitational physics as it applies to the dynamics of celestial bodies and the analysis of precise astronomical observations. In so doing, it fills the need for a textbook that teaches modern dynamical astronomy with a strong emphasis on the relativistic aspects of the subject produced by the curved geometry of four-dimensional spacetime. The first three chapters review the fundamental principles of celestial mechanics and of special and general relativity. This background material forms the basis for understanding relativistic r

  8. Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

    International Nuclear Information System (INIS)

    Marquette, Ian

    2011-01-01

    There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

  9. Diffeomorphism Group Representations in Relativistic Quantum Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Goldin, Gerald A. [Rutgers Univ., Piscataway, NJ (United States); Sharp, David H. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-12-20

    We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.

  10. 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

  11. Chaos in Dirac electron optics: Emergence of a relativistic quantum chimera

    OpenAIRE

    Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

    2018-01-01

    We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical ...

  12. Quantum mechanics, stochasticity and space-time

    International Nuclear Information System (INIS)

    Ramanathan, R.

    1986-04-01

    An extended and more rigorous version of a recent proposal for an objective stochastic formulation of quantum mechanics along with its extension to the relativistic case without spin is presented. The relativistic Klein-Gordon equation is shown to be a particular form of the relativistic Kolmogorov-Fokker-Planck equation which is derived from a covariant formulation of the Chapman-Kolmogorov condition. Complexification of probability amplitudes is again achieved only through a conformal rotation of Minkowski space-time M 4 . (author)

  13. Relativistic quantum information in detectors–field interactions

    International Nuclear Information System (INIS)

    Hu, B L; Lin, Shih-Yuin; Louko, Jorma

    2012-01-01

    We review Unruh–DeWitt detectors and other models of detector–field interaction in a relativistic quantum field theory setting as a tool for extracting detector–detector, field–field and detector–field correlation functions of interest in quantum information science, from entanglement dynamics to quantum teleportation. In particular, we highlight the contrast between the results obtained from linear perturbation theory which can be justified provided switching effects are properly accounted for, and the nonperturbative effects from available analytic expressions which incorporate the backreaction effects of the quantum field on the detector behavior. (paper)

  14. 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.

  15. Relativistic quantum Darwinism in Dirac fermion and graphene systems

    Science.gov (United States)

    Ni, Xuan; Huang, Liang; Lai, Ying-Cheng; Pecora, Louis

    2012-02-01

    We solve the Dirac equation in two spatial dimensions in the setting of resonant tunneling, where the system consists of two symmetric cavities connected by a finite potential barrier. The shape of the cavities can be chosen to yield both regular and chaotic dynamics in the classical limit. We find that certain pointer states about classical periodic orbits can exist, which are signatures of relativistic quantum Darwinism (RQD). These localized states suppress quantum tunneling, and the effect becomes less severe as the underlying classical dynamics in the cavity is chaotic, leading to regularization of quantum tunneling. Qualitatively similar phenomena have been observed in graphene. A physical theory is developed to explain relativistic quantum Darwinism and its effects based on the spectrum of complex eigenenergies of the non-Hermitian Hamiltonian describing the open cavity system.

  16. 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

  17. Relativistic quantum correlations in bipartite fermionic states

    Indian Academy of Sciences (India)

    The influences of relative motion, the size of the wave packet and the average momentum of the particles on different types of correlations present in bipartite quantum states are investigated. In particular, the dynamics of the quantum mutual information, the classical correlation and the quantum discord on the ...

  18. Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera.

    Science.gov (United States)

    Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

    2018-03-23

    We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting-henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

  19. Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera

    Science.gov (United States)

    Xu, Hong-Ya; Wang, Guang-Lei; Huang, Liang; Lai, Ying-Cheng

    2018-03-01

    We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting—henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

  20. Lorentz-covariant reduced-density-operator theory for relativistic-quantum-information processing

    International Nuclear Information System (INIS)

    Ahn, Doyeol; Lee, Hyuk-jae; Hwang, Sung Woo

    2003-01-01

    In this paper, we derived a Lorentz-covariant quantum Liouville equation for the density operator which describes the relativistic-quantum-information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced density operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of the nonrelativistic case, which is valid only in some specified reference frame. To show that our formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and could be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics

  1. 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.

  2. The relativistic virial theorem

    International Nuclear Information System (INIS)

    Lucha, W.; Schoeberl, F.F.

    1989-11-01

    The relativistic generalization of the quantum-mechanical virial theorem is derived and used to clarify the connection between the nonrelativistic and (semi-)relativistic treatment of bound states. 12 refs. (Authors)

  3. 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...

  4. Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics

    CERN Document Server

    Arai, A

    2006-01-01

    A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral $\\int_{{\\bf R}^3}^\\oplus\\overline{H({\\bf p})}d{\\bf p}$ of a family of self-adjoint operators $\\overline{H({\\bf p})}$ acting in the Hilbert space $\\oplus^4{\\cal F}_{\\rm rad}$, where ${\\cal F}_{\\rm rad}$ is the Hilbert space of the quantum radiation field. The fibre operator $\\overline{H({\\bf p})}$ is called the Hamiltonian of the Dirac polaron with total momentum ${\\bf p} \\in {\\bf R}^3$. The main result of this paper is concerned with the non-relativistic (scaling) limit of $\\overline{H({\\bf p})}$. It is proven that the non-relativistic limit of $\\overline{H({\\bf p})}$ yields a self-adjoint extension of a Hamiltonian of a polaron with spin $1/2$ in non-relativistic quantum electrodynamics.

  5. Experiments in PT-symmetric quantum mechanics

    Czech Academy of Sciences Publication Activity Database

    Znojil, Miloslav

    2004-01-01

    Roč. 54, č. 1 (2004), s. 151-156 ISSN 0011-4626 R&D Projects: GA AV ČR IAA1048302 Institutional research plan: CEZ:AV0Z1048901 Keywords : quantum mechanics * relativistic kinematics * non-Hermitian observables Subject RIV: BE - Theoretical Physics Impact factor: 0.292, year: 2004

  6. Weyl consistency conditions in non-relativistic quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Pal, Sridip; Grinstein, Benjamín [Department of Physics, University of California,San Diego, 9500 Gilman Drive, La Jolla, CA 92093 (United States)

    2016-12-05

    Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2+1 dimensions with anisotropic scaling exponent z=2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. We comment on possible candidates for a C-theorem in higher dimensions.

  7. 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

  8. On relativistic irreducible quantum fields fulfilling CCR

    International Nuclear Information System (INIS)

    Baumann, K.

    1987-01-01

    Let phi be a relativistic scalar field fulfilling canonical commutation relations (CCR). Furthermore it is assumed that the time zero fields and momenta form an irreducible set. Based on estimates given by Herbst [I. W. Herbst, J. Math. Phys. 17, 1210 (1976)], and by methods developed by Powers [R. T. Powers, Commun. Math. Phys. 4, 145 (1967)], it is shown that phi has to be a free field in n>3 space dimensions. For n = 3 (resp. n = 2) restrictions that look similar to the restriction in a formal :phi 4 : 3 /sub +/ 1 (resp. :phi 6 : 2 /sub +/ 1 ) theory are obtained

  9. Local relativistic invariant flows for quantum fields

    International Nuclear Information System (INIS)

    Albeverio, S.; Hoeegh-Krahn, R.; Sirugue, M.

    1983-01-01

    For quantum fields with trigonometric interaction in arbitrary space dimension we construct a representation of the Lorentz group by automorphisms on a Banach space generated by the Weyl algebra. (orig.)

  10. An introduction to relativistic quantum field theory

    CERN Document Server

    Schweber, Silvan S

    1961-01-01

    Complete, systematic, and self-contained, this text introduces modern quantum field theory. "Combines thorough knowledge with a high degree of didactic ability and a delightful style." - Mathematical Reviews. 1961 edition.

  11. 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.)

  12. 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.)

  13. Free space relativistic quantum cryptography with faint laser pulses

    International Nuclear Information System (INIS)

    Molotkov, S N; Potapova, T A

    2013-01-01

    A new protocol for quantum key distribution through empty space is proposed. Apart from the quantum mechanical restrictions on distinguishability of non-orthogonal states, the protocol employs additional restrictions imposed by special relativity. The protocol ensures generation of a secure key even for the source generating non-strictly single-photon quantum states and for arbitrary losses in quantum communication channel. (letter)

  14. 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

  15. Relativistic quantum games in noninertial frames

    Energy Technology Data Exchange (ETDEWEB)

    Khan, Salman; Khan, M Khalid, E-mail: sksafi@phys.qau.edu.pk [Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan)

    2011-09-02

    We study the influence of the Unruh effect on quantum non-zero sum games. In particular, we investigate the quantum Prisoners' Dilemma both for entangled and unentangled initial states and show that the acceleration of the noninertial frames disturbs the symmetry of the game. It is shown that for the maximally entangled initial state, the classical strategy C-hat (cooperation) becomes the dominant strategy. Our investigation shows that any quantum strategy does no better for any player against the classical strategies. The miracle move of Eisert et al (1999 Phys. Rev. Lett.83 3077) is no more a superior move. We show that the dilemma-like situation is resolved in favor of one player or the other. (paper)

  16. Relativistic quantum games in noninertial frames

    International Nuclear Information System (INIS)

    Khan, Salman; Khan, M Khalid

    2011-01-01

    We study the influence of the Unruh effect on quantum non-zero sum games. In particular, we investigate the quantum Prisoners' Dilemma both for entangled and unentangled initial states and show that the acceleration of the noninertial frames disturbs the symmetry of the game. It is shown that for the maximally entangled initial state, the classical strategy C-hat (cooperation) becomes the dominant strategy. Our investigation shows that any quantum strategy does no better for any player against the classical strategies. The miracle move of Eisert et al (1999 Phys. Rev. Lett.83 3077) is no more a superior move. We show that the dilemma-like situation is resolved in favor of one player or the other. (paper)

  17. 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.

  18. 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

  19. Dielectric response of planar relativistic quantum plasmas

    International Nuclear Information System (INIS)

    Bardos, D.C.; Frankel, N.E.

    1991-01-01

    The dielectric response of planar relativistic charged particle-antiparticle plasmas is investigated, treating Fermi and Bose plasmas. The conductivity tensor in each case is derived in the self-consistent Random Phase Approximation. The tensors are then evaluated at zero temperature for the case of no external fields, leading to explicit dispersion relations for the electrodynamic modes of the plasma. The longitudinal and transverse modes are in general coupled for plasma layers. This coupling vanishes, however, in the zero field case, allowing 'effective' longitudinal and transverse dielectric functions to be defined in terms of components of the conductivity tensor. Solutions to the longitudinal mode equations (i.e. plasmon modes) are exhibited, while purely transverse modes are found not to exist. In the case of the Bose plasma the screening of a test charge is investigated in detail. 41 refs., 1 fig

  20. Relativistic quantum correlations in bipartite fermionic states

    Indian Academy of Sciences (India)

    2016-09-21

    Sep 21, 2016 ... particles on different types of correlations present in bipartite quantum states are investigated. In particular, the ... the focus of research for the last few years. Many re- ..... figures, the qualitative behaviour of all the three types ...

  1. 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

  2. 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.

  3. 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

  4. 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

  5. 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...

  6. 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).

  7. 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)

  8. 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.

  9. 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.

  10. Relativistic Celestial Mechanics of the Solar System

    Science.gov (United States)

    Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George

    2011-09-01

    The general theory of relativity was developed by Einstein a century ago. Since then, it has become the standard theory of gravity, especially important to the fields of fundamental astronomy, astrophysics, cosmology, and experimental gravitational physics. Today, the application of general relativity is also essential for many practical purposes involving astrometry, navigation, geodesy, and time synchronization. Numerous experiments have successfully tested general relativity to a remarkable level of precision. Exploring relativistic gravity in the solar system now involves a variety of high-accuracy techniques, for example, very long baseline radio interferometry, pulsar timing, spacecraft Doppler tracking, planetary radio ranging, lunar laser ranging, the global positioning system (GPS), torsion balances and atomic clocks. Over the last few decades, various groups within the International Astronomical Union have been active in exploring the application of the general theory of relativity to the modeling and interpretation of high-accuracy astronomical observations in the solar system and beyond. A Working Group on Relativity in Celestial Mechanics and Astrometry was formed in 1994 to define and implement a relativistic theory of reference frames and time scales. This task was successfully completed with the adoption of a series of resolutions on astronomical reference systems, time scales, and Earth rotation models by the 24th General Assembly of the IAU, held in Manchester, UK, in 2000. However, these resolutions only form a framework for the practical application of relativity theory, and there have been continuing questions on the details of the proper application of relativity theory to many common astronomical problems. To ensure that these questions are properly addressed, the 26th General Assembly of the IAU, held in Prague in August 2006, established the IAU Commission 52, "Relativity in Fundamental Astronomy". The general scientific goals of the new

  11. 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.)

  12. 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�...

  13. Experimental considerations for quantum-entanglement studies with relativistic fermions

    Energy Technology Data Exchange (ETDEWEB)

    Schlemme, Steffen; Peck, Marius; Enders, Joachim [TU Darmstadt (Germany); Bodek, Kazimierz; Rozpedzik, Dagmara; Zejma, Jacek [Jagiellonian University, Cracow (Poland); Caban, Pawel; Rembielinski, Jakub [University of Lodz, Lodz (Poland); Ciborowski, Jacek; Dragowski, Michal; Wlodarczyk, Marta [Warsaw University, Warsaw (Poland); Kozela, Adam [Institute of Nuclear Physics, PAS, Cracow (Poland)

    2015-07-01

    The QUEST (Quantum entanglement of Ultra-relativistic Electrons in Singlet and Triplet states) project is aimed at the determination of the electron spin correlation function at relativistic energies. Electron pairs are created through Moeller scattering, and polarization observables are planned to be measured in Mott scattering. The predicted spin correlation function is energy dependent with values of several per cent at energies of 10-20 MeV. The results of a first test experiment at the S-DALINAC were not sensitive enough to detect entangled and Mott-scattered electron pairs at the expected energies. Further steps are either to improve the former setup or design a new polarimeter for lower energies to improve statistics due to the higher scattering cross sections. This contribution presents general considerations, test results, and an outlook.

  14. 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

  15. 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

  16. 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.

  17. 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.

  18. Stationary self-focusing of Gaussian laser beam in relativistic thermal quantum plasma

    International Nuclear Information System (INIS)

    Patil, S. D.; Takale, M. V.

    2013-01-01

    In the present paper, we have employed the quantum dielectric response in thermal quantum plasma to model relativistic self-focusing of Gaussian laser beam in a plasma. We have presented an extensive parametric investigation of the dependence of beam-width parameter on distance of propagation in relativistic thermal quantum plasma. We have studied the role of Fermi temperature in the phenomenon of self-focusing. It is found that the quantum effects cause much higher oscillations of beam-width parameter and better relativistic focusing of laser beam in thermal quantum plasma in comparison with that in the relativistic cold quantum plasma and classical relativistic plasma. Our computations show more reliable results in comparison to the previous works

  19. 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.

  20. 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

  1. 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

  2. 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

  3. Relativistic local quantum field theory for m=0 particles

    International Nuclear Information System (INIS)

    Morales Villasevil, A.

    1965-01-01

    A method is introduced ta deal with relativistic quantum field theory for particles with m=0. Two mappings I and J, giving rise respectively to particle and anti particle states, are defined between a test space and the physical Hilbert space. The intrinsic field operator is then defined as the minimal causal linear combinations of operators belonging to the annihilation-creation algebra associated to the germ and antigerm parts of the element. Local elements are introduced as improper test elements and local field operators are constructed in the same way as the intrinsic ones. Commutation rules are given. (Author) 17 refs

  4. Quantum mechanics in complex systems

    Science.gov (United States)

    Hoehn, Ross Douglas

    This document should be considered in its separation; there are three distinct topics contained within and three distinct chapters within the body of works. In a similar fashion, this abstract should be considered in three parts. Firstly, we explored the existence of multiply-charged atomic ions by having developed a new set of dimensional scaling equations as well as a series of relativistic augmentations to the standard dimensional scaling procedure and to the self-consistent field calculations. Secondly, we propose a novel method of predicting drug efficacy in hopes to facilitate the discovery of new small molecule therapeutics by modeling the agonist-protein system as being similar to the process of Inelastic Electron Tunneling Spectroscopy. Finally, we facilitate the instruction in basic quantum mechanical topics through the use of quantum games; this method of approach allows for the generation of exercises with the intent of conveying the fundamental concepts within a first year quantum mechanics classroom. Furthermore, no to be mentioned within the body of the text, yet presented in appendix form, certain works modeling the proliferation of cells types within the confines of man-made lattices for the purpose of facilitating artificial vascular transplants. In Chapter 2, we present a theoretical framework which describes multiply-charged atomic ions, their stability within super-intense laser fields, also lay corrections to the systems due to relativistic effects. Dimensional scaling calculations with relativistic corrections for systems: H, H-, H 2-, He, He-, He2-, He3- within super-intense laser fields were completed. Also completed were three-dimensional self consistent field calculations to verify the dimensionally scaled quantities. With the aforementioned methods the system's ability to stably bind 'additional' electrons through the development of multiple isolated regions of high potential energy leading to nodes of high electron density is shown

  5. 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

  6. 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.

  7. 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...

  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. 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.

  10. 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.))

  11. Conceptual evolution of Newtonian and relativistic mechanics

    CERN Document Server

    Ghosh, Amitabha

    2018-01-01

    This book provides an introduction to Newtonian and relativistic mechanics. Unlike other books on the topic, which generally take a 'top-down' approach, it follows a novel system to show how the concepts of the 'science of motion' evolved through a veritable jungle of intermediate ideas and concepts. Starting with Aristotelian philosophy, the text gradually unravels how the human mind slowly progressed towards the fundamental ideas of inertia physics. The concepts that now appear so obvious to even a high school student took great intellectuals more than a millennium to clarify. The book explores the evolution of these concepts through the history of science. After a comprehensive overview of the discovery of dynamics, it explores fundamental issues of the properties of space and time and their relation with the laws of motion. It also explores the concepts of spatio-temporal locality and fields, and offers a philosophical discussion of relative motion versus absolute motion, as well as the concept of an abso...

  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. Impact of Relativistic Electron Beam on Hole Acoustic Instability in Quantum Semiconductor Plasmas

    Science.gov (United States)

    Siddique, M.; Jamil, M.; Rasheed, A.; Areeb, F.; Javed, Asif; Sumera, P.

    2018-01-01

    We studied the influence of the classical relativistic beam of electrons on the hole acoustic wave (HAW) instability exciting in the semiconductor quantum plasmas. We conducted this study by using the quantum-hydrodynamic model of dense plasmas, incorporating the quantum effects of semiconductor plasma species which include degeneracy pressure, exchange-correlation potential and Bohm potential. Analysis of the quantum characteristics of semiconductor plasma species along with relativistic effect of beam electrons on the dispersion relation of the HAW is given in detail qualitatively and quantitatively by plotting them numerically. It is worth mentioning that the relativistic electron beam (REB) stabilises the HAWs exciting in semiconductor (GaAs) degenerate plasma.

  14. 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)

  15. 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 ...

  16. 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.

  17. 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

  18. 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.)

  19. 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

  20. Construction of relativistic quantum theory: a progress report

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1986-06-01

    We construct the particulate states of quantum physics using a recursive computer program that incorporates non-determinism by means of locally arbitrary choices. Quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G, connected to laboratory events via finite particle number scattering theory and the counter paradigm. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact

  1. 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.

  2. Support for the existence of invertible maps between electronic densities and non-analytic 1-body external potentials in non-relativistic time-dependent quantum mechanics

    Science.gov (United States)

    Mosquera, Martín A.

    2017-10-01

    Provided the initial state, the Runge-Gross theorem establishes that the time-dependent (TD) external potential of a system of non-relativistic electrons determines uniquely their TD electronic density, and vice versa (up to a constant in the potential). This theorem requires the TD external potential and density to be Taylor-expandable around the initial time of the propagation. This paper presents an extension without this restriction. Given the initial state of the system and evolution of the density due to some TD scalar potential, we show that a perturbative (not necessarily weak) TD potential that induces a non-zero divergence of the external force-density, inside a small spatial subset and immediately after the initial propagation time, will cause a change in the density within that subset, implying that the TD potential uniquely determines the TD density. In this proof, we assume unitary evolution of wavefunctions and first-order differentiability (which does not imply analyticity) in time of the internal and external force-densities, electronic density, current density, and their spatial derivatives over the small spatial subset and short time interval.

  3. Coherent states in quantum mechanics; Estados coerentes em mecanica quantica

    Energy Technology Data Exchange (ETDEWEB)

    Rodrigues, R. de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: rafaelr@cbpf.br; Fernandes Junior, Damasio; Batista, Sheyla Marques [Paraiba Univ., Campina Grande, PB (Brazil). Dept. de Engenharia Eletrica

    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)

  4. 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...

  5. Solution of relativistic quantum optics problems using clusters of graphical processing units

    Energy Technology Data Exchange (ETDEWEB)

    Gordon, D.F., E-mail: daviel.gordon@nrl.navy.mil; Hafizi, B.; Helle, M.H.

    2014-06-15

    Numerical solution of relativistic quantum optics problems requires high performance computing due to the rapid oscillations in a relativistic wavefunction. Clusters of graphical processing units are used to accelerate the computation of a time dependent relativistic wavefunction in an arbitrary external potential. The stationary states in a Coulomb potential and uniform magnetic field are determined analytically and numerically, so that they can used as initial conditions in fully time dependent calculations. Relativistic energy levels in extreme magnetic fields are recovered as a means of validation. The relativistic ionization rate is computed for an ion illuminated by a laser field near the usual barrier suppression threshold, and the ionizing wavefunction is displayed.

  6. 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.

  7. 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

  8. Studies of Ionic Photoionization Using Relativistic Random Phase Approximation and Relativistic Multichannel Quantum Defect Theory

    Science.gov (United States)

    Haque, Ghousia Nasreen

    The absorption of electromagnetic radiation by positive ions is one of the fundamental processes of nature which occurs in every intensely hot environment. Due to the difficulties in producing sufficient densities of ions in a laboratory, there are very few measurements of ionic photoabsorption parameters. On the theoretical side, some calculations have been made of a few major photoionization parameters, but generally speaking, most of the work done so far has employed rather simple single particle models and any theoretical work which has adequately taken into account intricate atomic many-body and relativistic effects is only scanty. In the present work, several complex aspects of atomic/ionic photoabsorption parameters have been studied. Non -resonant photoionization in neon and argon isonuclear as well as isoelectronic sequences has been studied using a very sophisticated technique, namely the relativistic random phase approximation (RRPA). This technique takes into account relativistic effects as well as an important class of major many-body effects on the same footing. The present calculations confirmed that gross features of photoionization parameters calculated using simpler models were not an artifact of the simple model. Also, the present RRPA calculations on K^+ ion and neutral Ar brought out the relative importance of various many-body effects such the inter-channel coupling. Inter-channel coupling between discrete bound state photoexcitation channels from an inner atomic/ionic level and photoionization continuum channels from an outer atomic/ionic level leads to the phenomena of autoionization resonances in the photoionization process. These resonances lead to very complex effects in the atomic/ionic photoabsorption spectra. These resonances have been calculated and studied in the present work in the neon and magnesium isoelectronic sequences using the relativistic multi-channel quantum defect theory (RMQDT) within the framework of the RRPA. The

  9. 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.

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

    International Nuclear Information System (INIS)

    Whitaker, A

    2004-01-01

    second book under consideration, that of Schwabl, contains 'Advanced' elements of quantum theory; it is designed for a course following on from one for which Gottfried and Yan, or Schwabl's own 'Quantum Mechanics' might be recommended. Many useful student problems are included. The presentation is said to be rigorous, but again this is a book for the physicist rather than the mathematician. The third book under consideration, that by Gustafson and Sigal is very different from the others. In academic level, at least the initial sections may actually be slightly lower; the book covers a one-term course taken by senior undergraduates or junior graduate students in mathematics or physics, and the initial chapters are on basic topics, such as the physical background, basic dynamics, observables and the uncertainty principle. However the level of mathematical sophistication is far higher than in the other books. While the mathematical prerequisites are modest, a third of the book is made up of what are called mathematical supplements. On the basis of these supplements, the level of mathematical sophistication and difficulty is increased substantially in the middle section of the book, where the topics considered are many-particle systems, density matrices, positive temperatures, the Feynman path integral, and quasi-classical analysis, and there is a final substantial step for the concluding chapters on resonances, an introduction to quantum field theory, and quantum electrodynamics of non-relativistic particles. A supplementary chapter contains an interesting approach to the renormalization group due to Bach, Froehlich and Sigal himself. This book is well-written, and the topics discussed have been well thought-out. It would provide a useful approach to quantum theory for the mathematician, and would also provide access for the physicist to some mathematically advanced methods and topics, but the physicist would definitely have to be prepared to work hard at the mathematics

  11. Response of a relativistic quantum magnetized electron gas

    International Nuclear Information System (INIS)

    Melrose, Donald B; Weise, Jeanette I

    2009-01-01

    The response 4-tensor is derived for a spin-independent, relativistic magnetized quantum electron gas. The sum over spins is carried out both directly and using a procedure due to Ritus. The 4-tensor components are written in terms of a sum over the two solutions of the resonance condition for the particle 4-momentum. It is shown that the dispersive properties may be described in terms of a single plasma dispersion function, for arbitrary occupation numbers for electrons and positrons in each Landau level. The plasma dispersion function is evaluated explicitly in the completely degenerate and nondegenerate thermal limits. The perpendicular wave number appears in the arguments of J-functions, which are proportional to generalized Laguerre polynomials, but not in the plasma dispersion function. The result generalizes a known form for the response tensor for parallel propagation (in the completely degenerate case), when the J-functions are either zero or unity, to arbitrary angles of propagation.

  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. Run-away electrons in relativistic spin (1) /(2) quantum electrodynamics

    International Nuclear Information System (INIS)

    Low, F.E.

    1998-01-01

    The existence of run-away solutions in classical and non-relativistic quantum electrodynamics is reviewed. It is shown that the less singular high energy behavior of relativistic spin (1) /(2) quantum electrodynamics precludes an analogous behavior in that theory. However, a Landau-like anomalous pole in the photon propagation function or in the electron-massive photon forward scattering amplitude would generate a new run-away, characterized by an energy scale ω∼m e thinspexp(1/α). This contrasts with the energy scale ω∼m e /α associated with the classical and non-relativistic quantum run-aways. copyright 1998 Academic Press, Inc

  14. Relativistic quantum vorticity of the quadratic form of the Dirac equation

    International Nuclear Information System (INIS)

    Asenjo, Felipe A; Mahajan, Swadesh M

    2015-01-01

    We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the Feynman–Gell-Mann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and non-relativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system. (paper)

  15. Solved and unsolved problems in relativistic quantum chemistry

    International Nuclear Information System (INIS)

    Kutzelnigg, Werner

    2012-01-01

    Graphical abstract: The graphical abstract represents the Dirac-Coulomb Hamiltonian in Fock space in a diagrammatic notation. A line (vertical or slanted) with an upgoing arrow represents an eletron, with a downgoing arrow a positron. A cross in the first line means the potential created by a nucleus, a broken line represents the Coulomb interaction between electrons and positrons. Highlights: ► Relativistic many-electron theory needs a Fock space and a field-dependent vacuum. ► A good starting point is QED in Coulomb gauge without transversal photons. ► The Dirac underworld picture is obsolete. ► A kinetically balanced even-tempered Gaussian basis is complete. ► ‘Quantum chemistry in Fock space is preferable over QED. - Abstract: A hierarchy of approximations in relativistic many-electron theory is discussed that starts with the Dirac equation and its expansion in a kinetically balanced basis, via a formulation of non-interacting electrons in Fock space (which is the only consistent way to deal with negative-energy states). The most straightforward approximate Hamiltonian for interacting electrons is derived from quantum electrodynamics (QED) in Coulomb gauge with the neglect of transversal photons. This allows an exact (non-perturbative) decoupling of the electromagnetic field from the fermionic field. The electric interaction of the fermions is non-retarded and non-quantized. The quantization of the fermionic field leads to a polarizable vacuum. The simplest (but somewhat problematic) approximation is a no-pair projected theory with external-field projectors. The Dirac-Coulomb operator in configuration space (first quantization) is not acceptable, even if the Brown–Ravenhall disease is much less virulent than often claimed. Effects of transversal photons, such as the Breit interaction and renormalized self-interaction can be taken care of perturbatively at the end, but there are still many open questions.

  16. 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.)

  17. 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.

  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. 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

  20. 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

  1. 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.)

  2. 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.

  3. 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...

  4. Introduction to the renormalization group study in relativistic quantum field theory

    International Nuclear Information System (INIS)

    Mignaco, J.A.; Roditi, I.

    1985-01-01

    An introduction to the renormalization group approach in relativistic quantum field theories is presented, beginning with a little historical about the subject. Further, this problem is discussed from the point of view of the perturbation theory. (L.C.) [pt

  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. Construction of relativistic quantum theory: a progress report

    Energy Technology Data Exchange (ETDEWEB)

    Noyes, H.P.

    1986-06-01

    We construct the particulate states of quantum physics using a recursive computer program that incorporates non-determinism by means of locally arbitrary choices. Quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G, connected to laboratory events via finite particle number scattering theory and the counter paradigm. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact.

  7. Symmetry and quantum mechanics

    CERN Document Server

    Corry, Scott

    2016-01-01

    This book offers an introduction to quantum mechanics for professionals, students, and others in the field of mathematics who have a minimal background in physics with an understanding of linear algebra and group theory. It covers such topics as Lie groups, algebras and their representations, and analysis (Hilbert space, distributions, the spectral Theorem, and the Stone-Von Neumann Theorem). The book emphasizes the role of symmetry and is useful to physicists as it provides a mathematical introduction to the topic.

  8. Relativistic quantum kinetic analysis of a pion--nucleon system

    International Nuclear Information System (INIS)

    Alonso, J.D.

    1985-01-01

    A relativistic plasma of nucleons interacting through pions via the usual isospin-invariant Yukawa coupling is analyzed in the framework of the covariant Wigner function technique. The method is manifestly covariant and the temperature effects are considered. The relativistic quantum BBGKY hierarchy for the pion--nucleon system is derived. By generalizing the Bogolioubov analysis of the classical BBGKY hierarchy a non-perturbative renormalizable method is elaborated which allows the solution of the kinetic problem in form of power series of two cluster parameters which measure the importance of correlations. In the lowest order of the cluster expansion (Hartree approximation of zero-order approximation) the quasi-nucleon Fock space is introduced, the fermion Wigner function in the thermodynamic equilibrium is obtained and the vacuum effects are renormalized. In this approximation the plasma behaves as a perfect Fermi gas of nucleons and antinucleons, but there exists an abnormal configuration with a uniform pion condensate which is unstable. In the next approximation (quadratic in the small parameters) the quasi-pion dispersion relation is obtained and the vacuum polarization tensor is renormalized. The quasi-pion rest-mass spectra (''plasma frequency'') and the effective-coupling behaviour as functions of the thermodynamic state are given. By estimating the size of the cluster parameters the self-consistency of the approximation scheme is proved. The quasi-pion Fock space is introduced and the quasi-pion equilibrium Wigner function is obtained. From these results the problem of the higher-order corrections to the Hartree thermodynamics is outlined

  9. 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

  10. BOOK REVIEWS: Quantum Mechanics: Fundamentals

    Science.gov (United States)

    Whitaker, A.

    2004-02-01

    , propagators, Green’s functions, semiclassical quantum mechanics. The level of mathematical rigour is stated as ‘typical of the bulk of theoretical physics literature---slovenly’; those unhappy with this are directed to the well-known books of Jordan and Thirring. The next chapter---‘Basic Tools’---explains a set of topics which students will need to use when studying particular systems---angular momentum and its addition, free particles, the two-body system, and the standard approximation techniques. There follow chapters on low-dimensional systems---harmonic oscillator, Aharanov--Bohm effect, one-dimensional scattering, WKB and so on; hydrogenic atoms---the Kepler problem, fine and hyperfine structure, Zeeman and Stark effects; and on two-electron atoms---spin and statistics. As in the first edition, there is a substantial treatment of symmetries, including time reversal, Galileo transformations, the rotation group, the Wigner-Eckart theorem and the Berry phase. There are two long chapters on scattering---elastic and inelastic respectively, including an account of the S matrix. The treatment of electrodynamics is much extended and modernised compared to that in the first edition. There are discussions of the quantization of the free field, causality and uncertainty in electrodynamics, vacuum fluctuations including the Casimir effect and the Lamb shift, and radiative transitions. There is a treatment of quantum optics, but this a only a brief introduction to a rapidly expanding subject, designed to facilitate understanding of the experiments on Bell’s inequalities discussed in the later chapter on interpretation. Other topics are the photoeffect in hydrogen, scattering of photons, resonant scattering and spontaneous decay. Identical particles are discussed, with a treatment of second quantization and an introduction to Bose--Einstein condensation, and the last chapter is a brief introduction to relativistic quantum mechanics, including the Dirac equation, the

  11. 10th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

    International Nuclear Information System (INIS)

    2017-01-01

    Preface The International Association for Relativistic Dynamics was organized in February 1998 in Houston, Texas, with John R. Fanchi as president. Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There, moreover, remained the important questions of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge’s book, The Relativistic Gas , and in Balescu’s book on relativistic statistical mechanics, and the development of a consistent single and many body relativistic quantum theory. In recent years, the very high accuracy of telescopes and advanced facilities for computation have brought a high level of interest in cosmological problems such as the structure of galaxies (dark matter) and the apparently anomalous expansion of the universe (dark energy). Some of the papers reported here deal with these problems, as well as other fundamental related issues. It was for this purpose, to bring together researchers from a wide variety of fields, such as particle physics, astrophysics, cosmology, foundations of relativity theory, and mathematical physics, with a common interest in relativistic dynamics, to investigate fundamental questions of

  12. Quantum dynamics characteristic and the flow of information for an open quantum system under relativistic motion

    Science.gov (United States)

    Sun, Wen-Yang; Wang, Dong; Fang, Bao-Long; Ye, Liu

    2018-03-01

    In this letter, the dynamics characteristics of quantum entanglement (negativity) and distinguishability (trace distance), and the flow of information for an open quantum system under relativistic motion are investigated. Explicitly, we propose a scenario that a particle A held by Alice suffers from an amplitude damping (AD) noise in a flat space-time and another particle B by Bob entangled with A travels with a fixed acceleration under a non-inertial frame. The results show that quantum distinguishability and entanglement are very vulnerable and fragile under the collective influence of AD noise and Unruh effect. Both of them will decrease with the growing intensity of the Unruh effect and the AD thermal bath. It means that the abilities of quantum distinguishability and entanglement to suppress the collective decoherence (AD noise and Unruh effect) are very weak. Furthermore, it turns out that the reduced quantum distinguishability of Alice’s system and Bob in the physically accessible region is distributed to another quantum distinguishability for Alice’s environment and Bob in the physically inaccessible region. That is, the information regarding the scenario is that the lost quantum distinguishability, as a fixed information, flows from the systems to the collective decoherence environment.

  13. Relativistic classical and quantum dynamics in intense crossed laser beams of various polarizations

    Directory of Open Access Journals (Sweden)

    M. Verschl

    2007-02-01

    Full Text Available The dynamics of an electron in crossed laser fields is investigated analytically. Two different standing wave configurations are compared. The counterpropagating laser waves are either linearly or circularly polarized. Both configurations have in common that there are one-dimensional trajectories on which the electron can oscillate with vanishing Lorentz force. The dynamics is analyzed for the situations when the electron moves in the vicinity of these ideal axes. If the laser intensities imply nonrelativistic electron dynamics, the system is described quantum mechanically. A semiclassical treatment renders the strongly relativistic regime accessible as well. To describe relativistic wave packets, the results of the classical analysis are employed for a Monte Carlo ensemble. This allows for a comparison of the wave packet dynamics for both configurations in the strongly relativistic regime. It is found for certain cases that relativity slows down the dynamics, i.e., for higher laser intensities, wave packet spreading and the drift away from the ideal axis of vanishing Lorentz force are shown to be increasingly suppressed.

  14. Relativistic particle in a box

    OpenAIRE

    Alberto, P.; Fiolhais, Carlos; Gil, Victor

    1996-01-01

    The problem of a relativistic spin 1/2 particle confined to a one-dimensional box is solved in a way that resembles closely the solution of the well known quantum-mechanical textbook problem of a non-relativistic particle in a box. The energy levels and probability density are computed and compared with the non-relativistic case

  15. 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.)

  16. 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...

  17. A reinterpretation of quantum mechanics

    International Nuclear Information System (INIS)

    Anastasov, A.H.

    1983-01-01

    A solution of the problem of corpuscular-wave dualism is proposed. It consists in the establishment of a continual-discrete, stochastic-deterministic space-time model of the 'particle in a quantum-mechanical sense'. This solution differs radically from the so-called Copenhagen interpretation. It has points of contact with de Broglie's double solution as well as with the fluid models, but avoids their shortcomings. The main shortcoming of the double solution is that it retains the particle's trajectory while in the fluid models there is no trace dicreteness. Moreover, when two or more interacting particles are involved, the wave function and the corresponding fluid both lose their physical reality, being defined in a configurational rather than in a real physical space. The corpuscular-wave object described here is called POLLETRON. Mathematically this is a pair of geometric objects in the space-time of the relativity theory. At the partial expense of depth and naturalness, a poletron can also be described classically, although its behaviour runs counter to the classical rules. This non-relativistic description based on the notion of a QUANTON is given here. A QUANTON is a classical particle (material point) which, however, is supershortliving (a 'particle-phantom')

  18. 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.)

  19. Postulates of quantum mechanics

    International Nuclear Information System (INIS)

    Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.

    1977-01-01

    Postulates of quantum mechanics and physical interpretation on observables and their measurement are presented. The physical content of Schroedinger equation, the superposition principle and the physical forecastings are also exposed. In complement are also presented: physical study of a particle in a infinite potential well; study of probability current; mean deviations of two conjugate observables; measurements on a part only of a physical system; density operator; evolution operator; Heisenberg and Schoredinger pictures; gauge invariance; propagator of the Schroedinger equation; unsteady levels lifetime; bound states of a particle in a potential well of any shape; non-bound states of a particle in a well or a potential barrier of some shape; quantum properties of a particle in a one-dimensional periodic structure [fr

  20. Proper-time quantum-mechanics and the Klein paradox

    International Nuclear Information System (INIS)

    Thaller, B.

    1981-01-01

    Scattering at high potential-steps is treated in the framework of relativistic proper-time theory. No paradox arises in contrast to Dirac's wavemechanics (''Klein's paradox''); pair creation may happen with a certain probability and may be described as a scattering process with ordinary quantum-mechanical methods. (author)

  1. On the definition of time operator in quantum mechanics

    International Nuclear Information System (INIS)

    Nowicki, A.A.

    1974-01-01

    Different approaches to the quantum-mechanical definition of time operator T are briefly discussed. In particular we define the analytic continuation of the time operator and show that one can construct its exact eigenstates. We consider also the case of a relativistic free scalar particle and discuss the notion of proper time operator S. (author)

  2. 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...

  3. 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...

  4. Quantum mechanics non-relativistic theory

    CERN Document Server

    Landau, Lev Davidovich

    1977-01-01

    This edition has been completely revised to include some 20% of new material. Important recent developments such as the theory of Regge poles are now included. Many problems with solutions have been added to those already contained in the book.

  5. Quantum mechanical signature in exclusive coherent pion production

    Science.gov (United States)

    Deutchman, P. A.; Buvel, R. L.; Maung, K. M.; Norbury, J. W.; Townsend, L. W.

    1986-01-01

    We calculate the coherent production of pions from subthreshold to relativistic energies in heavy-ion collisions using a quantum, microscopic, many-body model. For the first time, in this approach, we use harmonic oscillator wave functions to describe shell-model information. The theoretical quantum mechanical results obtained for the pion spectra represent an important improvement over our previous microscopic, many-body calculations.

  6. 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

  7. Arbitrary amplitude nucleus-acoustic solitons in multi-ion quantum plasmas with relativistically degenerate electrons

    Science.gov (United States)

    Sultana, S.; Schlickeiser, R.

    2018-02-01

    A three component degenerate relativistic quantum plasma (consisting of relativistically degenerate electrons, nondegenerate inertial light nuclei, and stationary heavy nuclei) is considered to model the linear wave and also the electrostatic solitary waves in the light nuclei-scale length. A well-known normal mode analysis is employed to investigate the linear wave properties. A mechanical-motion analog (Sagdeev-type) pseudo-potential approach, which reveals the existence of large amplitude solitary excitations, is adopted to study the nonlinear wave properties. Only the positive potential solitary excitations are found to exist in the plasma medium under consideration. The basic properties of the arbitrary amplitude electrostatic acoustic modes in the light nuclei-scale length and their existence domain in terms of soliton speed (Mach number) are examined. The modifications of solitary wave characteristics and their existence domain with the variation of different key plasma configuration parameters (e.g., electrons degeneracy parameter, inertial light nuclei number density, and degenerate electron number density) are also analyzed. Our results, which may be helpful to explain the basic features of the nonlinear wave propagation in multi-component degenerate quantum plasmas, in connection with astrophysical compact objects (e.g., white dwarfs) are briefly discussed.

  8. Quantum mechanics of leptogenesis

    Energy Technology Data Exchange (ETDEWEB)

    Mendizabal Cofre, Sebastian

    2010-08-15

    Leptogenesis is an attractive mechanism that simultaneously explains the matterantimatter asymmetry of the universe as well as the small masses of the standard model neutrinos. This is performed by naturally extending the standard model with the insertion of right handed neutrinos. Leptogenesis is usually studied via the semi-classical Boltzmann equations. However, these equations suffer from basic conceptual problems and they lack to include many quantum phenomena, such as memory effects and coherence oscillations. In order to fully describe leptogenesis, a full quantum treatment is required. In this work we show how to address leptogenesis systematically in a purely quantum way. We start by studying scalar and fermionic excitations in a plasma by solving the Kadanoff-Baym equations of motion for Green's functions, with significant emphasis on the initial and boundary conditions of the solutions. We compute analytically the asymmetry generated from the departure of equilibrium of a particle in a thermal bath. The comparison with the semi-classical Boltzmann approach is also analysed, leading to a qualitative difference between both methods. The non-locality of the Kadanoff-Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry, effects that cannot be studied with the Boltzmann equations. The insertion of standard model interactions like the decay widths for the particles of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes, i.e. we regain the Boltzmann equations. (orig.)

  9. Quantum mechanics of leptogenesis

    International Nuclear Information System (INIS)

    Mendizabal Cofre, Sebastian

    2009-07-01

    Leptogenesis is an attractive mechanism that simultaneously explains the matterantimatter asymmetry of the universe as well as the small masses of the standard model neutrinos. This is performed by naturally extending the standard model with the insertion of right handed neutrinos. Leptogenesis is usually studied via the semi-classical Boltzmann equations. However, these equations suffer from basic conceptual problems and they lack to include many quantum phenomena, such as memory effects and coherence oscillations. In order to fully describe leptogenesis, a full quantum treatment is required. In this work we show how to address leptogenesis systematically in a purely quantum way. We start by studying scalar and fermionic excitations in a plasma by solving the Kadanoff-Baym equations of motion for Green's functions, with significant emphasis on the initial and boundary conditions of the solutions. We compute analytically the asymmetry generated from the departure of equilibrium of a particle in a thermal bath. The comparison with the semi-classical Boltzmann approach is also analysed, leading to a qualitative difference between both methods. The non-locality of the Kadanoff-Baym equations shows how off-shell effects can have a huge impact on the generated asymmetry, effects that cannot be studied with the Boltzmann equations. The insertion of standard model interactions like the decay widths for the particles of the bath is also discussed. We explain how with a trivial insertion of these widths we regain locality on the processes, i.e. we regain the Boltzmann equations. (orig.)

  10. Quantum mechanical resonances

    International Nuclear Information System (INIS)

    Cisneros S, A.; McIntosh, H.V.

    1982-01-01

    A discussion of the nature of quantum mechanical resonances is presented from the point of view of the spectral theory of operators. In the case of Bohr-Feshbach resonances, graphs are presented to illustrate the theory showing the decay of a doubly excited metastable state and the excitation of the resonance by an incident particle with proper energy. A characterization of resonances is given as well as a procedure to determine widths using the spectral density function. A sufficient condition is given for the validity of the Breit-Wigner formula for Bohr-Feshbach resonances. (author)

  11. 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

  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. Mechanism of 238U disintegration induced by relativistic particles

    International Nuclear Information System (INIS)

    Andronenko, L.N.; Zhdanov, A.A.; Kravtsov, A.V.; Solyakin, G.E.

    2002-01-01

    In heavy-nucleus disintegration induced by a relativistic projectile particle, the production of collinear massive fragments accompanied by numerous charged particles and neutrons is explained in terms of the mechanism of projectile-momentum compensation due to the emission of a particle whose mass is greater than the projectile mass

  14. Quantum mechanics versus relativity: an experimental test of the structure of spacetime

    International Nuclear Information System (INIS)

    Emelyanov, S A

    2012-01-01

    We have performed an experimental test under the conditions in which quantum mechanics predicts spatially discontinuous single-particle transport. The transport is beyond the relativistic paradigm of movement in Cartesian space and therefore may well be nonlocal. Our test has demonstrated that such transport does exist. This fact opens the door for a realistic interpretation of quantum mechanics in so far as the requirement of Lorentz invariance appears inapplicable to any version of quantum theory. Moreover, as quantum mechanics proposes a particle dynamics beyond relativity, it automatically requires an adequate ‘quantum’ concept of spacetime, for which the relativistic concept is only a limiting case. The quantum concept allows absolute simultaneity and hence revives the notion of absolute time. It also goes beyond the relativistic curvilinear Cartesian order of space to account for quantum phenomena such as discontinuity and nonlocality in the spirit of Bohm's concept of the implicate order.

  15. 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

  16. 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

  17. 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.)

  18. 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

  19. 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.)

  20. Investigations on quantum mechanics with minimal length

    International Nuclear Information System (INIS)

    Chargui, Yassine

    2009-01-01

    We consider a modified quantum mechanics where the coordinates and momenta are assumed to satisfy a non-standard commutation relation of the form( X i , P j ) = iℎ(δ ij (1+βP 2 )+β'P i P j ). Such an algebra results in a generalized uncertainty relation which leads to the existence of a minimal observable length. Moreover, it incorporates an UV/IR mixing and non commutative position space. We analyse the possible representations in terms of differential operators. The latter are used to study the low energy effects of the minimal length by considering different quantum systems : the harmonic oscillator, the Klein-Gordon oscillator, the spinless Salpeter Coulomb problem, and the Dirac equation with a linear confining potential. We also discuss whether such effects are observable in precision measurements on a relativistic electron trapped in strong magnetic field.

  1. 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.

  2. 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.

  3. Quantum Geometry: Relativistic energy approach to cooperative electron-nucleary-transition spectrum

    Directory of Open Access Journals (Sweden)

    Ольга Юрьевна Хецелиус

    2014-11-01

    Full Text Available An advanced relativistic energy approach is presented and applied to calculating parameters of electron-nuclear 7-transition spectra of nucleus in the atom. The intensities of the spectral satellites are defined in the relativistic version of the energy approach (S-matrix formalism, and gauge-invariant quantum-electrodynamical perturbation theory with the Dirac-Kohn-Sham density-functional zeroth approximation.

  4. 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.

  5. Quantum mechanics of a photon

    Science.gov (United States)

    Babaei, Hassan; Mostafazadeh, Ali

    2017-08-01

    A first-quantized free photon is a complex massless vector field A =(Aμ ) whose field strength satisfies Maxwell's equations in vacuum. We construct the Hilbert space H of the photon by endowing the vector space of the fields A in the temporal-Coulomb gauge with a positive-definite and relativistically invariant inner product. We give an explicit expression for this inner product, identify the Hamiltonian for the photon with the generator of time translations in H , determine the operators representing the momentum and the helicity of the photon, and introduce a chirality operator whose eigenfunctions correspond to fields having a definite sign of energy. We also construct a position operator for the photon whose components commute with each other and with the chirality and helicity operators. This allows for the construction of the localized states of the photon with a definite sign of energy and helicity. We derive an explicit formula for the latter and compute the corresponding electric and magnetic fields. These turn out to diverge not just at the point where the photon is localized but on a plane containing this point. We identify the axis normal to this plane with an associated symmetry axis and show that each choice of this axis specifies a particular position operator, a corresponding position basis, and a position representation of the quantum mechanics of a photon. In particular, we examine the position wave functions determined by such a position basis, elucidate their relationship with the Riemann-Silberstein and Landau-Peierls wave functions, and give an explicit formula for the probability density of the spatial localization of the photon.

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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.

  11. 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)

  12. 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...

  13. 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)

  14. Propagation of a TE surface mode in a relativistic electron beam–quantum plasma system

    International Nuclear Information System (INIS)

    Abdel Aziz, M.

    2012-01-01

    The dispersion properties of a transverse electric (TE) surface waves propagating along the interface between a magneto-quantum plasma–relativistic beam system and vacuum are studied by using the quantum hydrodynamic model. The general dispersion relations are derived and analyzed in some special cases of interest. Moreover, the effects of density gradients for the beam and plasma on the dispersion properties of surface waves are investigated. The kind of dispersion relations depends strongly on the ambient magnetic field B o via the gyro-frequency ω c , the quantum parameters, and the width of the plasma layer as well as the relativistic factor for the electron beam. It is found that the quantum effects play a crucial role to facilitate the propagation of TE surface waves. -- Highlights: ► Propagation of TE surface waves on bounded magneto-quantum plasma by relativistic beam is studied. ► The quantum plasma consists of transitional layer adjacent to uniform layer. ► Influence of quantum effects on the propagation of TE surface waves are taken into account. ► Effects of homogeneity and inhomogeneity for beam on TE surface waves are considered. ► It is found that quantum effects facilitate the propagation of TE surface modes.

  15. Relativistic quantum thermodynamics of ideal gases in two dimensions.

    Science.gov (United States)

    Blas, H; Pimentel, B M; Tomazelli, J L

    1999-11-01

    In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.

  16. Relativistic Quantum Thermodynamics of Ideal Gases in 2 Dimensions

    OpenAIRE

    Blas, H.; Pimentel, B. M.; Tomazelli, J. L.

    1999-01-01

    In this work we study the behavior of relativistic ideal Bose and Fermi gases in two space dimensions. Making use of polylogarithm functions we derive a closed and unified expression for their densities. It is shown that both type of gases are essentially inequivalent, and only in the non-relativistic limit the spinless and equal mass Bose and Fermi gases are equivalent as known in the literature.

  17. 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

  18. 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.

  19. 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 ...

  20. 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 ...

  1. Quantum mechanics and experience

    CERN Document Server

    Albert, David Z

    1992-01-01

    The more science tells us about the world, the stranger it looks. Ever since physics first penetrated the atom, early in this century, what it found there has stood as a radical and unanswered challenge to many of our most cherished conceptions of nature. It has literally been called into question since then whether or not there are always objective matters of fact about the whereabouts of subatomic particles, or about the locations of tables and chairs, or even about the very contents of our thoughts. A new kind of uncertainty has become a principle of science. This book is an original and provocative investigation of that challenge, as well as a novel attempt at writing about science in a style that is simultaneously elementary and deep. It is a lucid and self-contained introduction to the foundations of quantum mechanics, accessible to anyone with a high school mathematics education, and at the same time a rigorous discussion of the most important recent advances in our understanding of that subject, some...

  2. 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.

  3. 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.

  4. Relativistic celestial mechanics with PPN parameters

    Science.gov (United States)

    Klioner, Sergei A.; Soffel, Michael H.

    2000-07-01

    Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters γ and β we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to η=4β-γ-3 reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in general relativity. We also show that the tidal gravitational field as seen in the local PPN reference system can be expanded into powers of local coordinates similar to the tidal expansion in general relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle (an Earth satellite) in that system. The translational and rotational equations of motion for center of mass and spin of each of N extended massive bodies possessing arbitrary multipole structure are derived. All equations of motion are presented also in the form of multipole expansions. Several interesting features of the equations are discussed. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived. For the first time, these equations are derived in a self-consistent manner which does not require any additional assumptions about the behavior of bodies such as secular stationarity.

  5. 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.

  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. 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

  8. Relativistic n-body wave equations in scalar quantum field theory

    International Nuclear Information System (INIS)

    Emami-Razavi, Mohsen

    2006-01-01

    The variational method in a reformulated Hamiltonian formalism of Quantum Field Theory (QFT) is used to derive relativistic n-body wave equations for scalar particles (bosons) interacting via a massive or massless mediating scalar field (the scalar Yukawa model). Simple Fock-space variational trial states are used to derive relativistic n-body wave equations. The equations are shown to have the Schroedinger non-relativistic limits, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Some examples of approximate ground state solutions of the n-body relativistic equations are obtained for various strengths of coupling, for both massive and massless mediating fields

  9. Fully nonlinear heavy ion-acoustic solitary waves in astrophysical degenerate relativistic quantum plasmas

    Science.gov (United States)

    Sultana, S.; Schlickeiser, R.

    2018-05-01

    Fully nonlinear features of heavy ion-acoustic solitary waves (HIASWs) have been investigated in an astrophysical degenerate relativistic quantum plasma (ADRQP) containing relativistically degenerate electrons and non-relativistically degenerate light ion species, and non-degenerate heavy ion species. The pseudo-energy balance equation is derived from the fluid dynamical equations by adopting the well-known Sagdeev-potential approach, and the properties of arbitrary amplitude HIASWs are examined. The small amplitude limit for the propagation of HIASWs is also recovered. The basic features (width, amplitude, polarity, critical Mach number, speed, etc.) of HIASWs are found to be significantly modified by the relativistic effect of the electron species, and also by the variation of the number density of electron, light ion, and heavy ion species. The basic properties of HIASWs, that may propagated in some realistic astrophysical plasma systems (e.g., in white dwarfs), are briefly discussed.

  10. 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.

  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. 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

  13. 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

  14. 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

  15. 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)

  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. 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.

  18. 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.)

  19. 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

  20. 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...

  1. 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.

  2. Quantum spin correlations in relativistic Møller scattering

    Directory of Open Access Journals (Sweden)

    Caban Paweł

    2017-01-01

    Full Text Available We present the relativistic spin correlation function (and the corresponding probabilities for a pair of polarized electrons originating from the Moller scattering. This particular state is easy to prepare experimentally; therefore, the results are discussed in view of a possible measurement. We also discuss the state after the Moller scattering in terms of entanglement and polarization transfer.

  3. 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...

  4. Quantum mechanics and field theory with fractional spin and statistics

    International Nuclear Information System (INIS)

    Forte, S.

    1992-01-01

    Planar systems admit quantum states that are neither bosons nor fermions, i.e., whose angular momentum is neither integer nor half-integer. After a discussion of some examples of familiar models in which fractional spin may arise, the relevant (nonrelativistic) quantum mechanics is developed from first principles. The appropriate generalization of statistics is also discussed. Some physical effects of fractional spin and statistics are worked out explicitly. The group theory underlying relativistic models with fractional spin and statistics is then introduced and applied to relativistic particle mechanics and field theory. Field-theoretical models in 2+1 dimensions are presented which admit solitons that carry fractional statistics, and are discussed in a semiclassical approach, in the functional integral approach, and in the canonical approach. Finally, fundamental field theories whose Fock states carry fractional spin and statistics are discussed

  5. 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

  6. 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.

  7. In search of a primitive ontology for relativistic quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Lam, Vincent [University of Lausanne, CH-1015 Lausanne (Switzerland)

    2014-07-01

    There is a recently much discussed approach to the ontology of quantum mechanics according to which the theory is ultimately about entities in 3-dimensional space and their temporal evolution. Such an ontology postulating from the start matter localized in usual physical space or spacetime, by contrast to an abstract high-dimensional space such as the configuration space of wave function realism, is called primitive ontology in the recent literature on the topic and finds its roots in Bell's notion of local beables. The main motivation for a primitive ontology lies in its explanatory power: the primitive ontology allows for a direct account of the behaviour and properties of familiar macroscopic objects. In this context, it is natural to look for a primitive ontology for relativistic quantum field theory (RQFT). The aim of this talk is to critically discuss this interpretative move within RQFT, in particular with respect to the foundational issue of the existence of unitarily inequivalent representations. Indeed the proposed primitive ontologies for RQFT rely either on a Fock space representation or a wave functional representation, which are strictly speaking only unambiguously available for free systems in flat spacetime. As a consequence, it is argued that these primitive ontologies constitute only effective ontologies and are hardly satisfying as a fundamental ontology for RQFT.

  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. 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

  10. Angularly Deformed Special Relativity and its Results for Quantum Mechanics

    OpenAIRE

    Glinka, Lukasz Andrzej

    2015-01-01

    In this paper, the deformed Special Relativity, which leads to an essentially new theoretical context of quantum mechanics, is presented. The formulation of the theory arises from a straightforward analogy with the Special Relativity, but its foundations are laid through the hypothesis on breakdown of the velocity-momentum parallelism which affects onto the Einstein equivalence principle between mass and energy of a relativistic particle. Furthermore, the derivation is based on the technique ...

  11. Generalized Poisson processes in quantum mechanics and field theory

    International Nuclear Information System (INIS)

    Combe, P.; Rodriguez, R.; Centre National de la Recherche Scientifique, 13 - Marseille; Hoegh-Krohn, R.; Centre National de la Recherche Scientifique, 13 - Marseille; Sirugue, M.; Sirugue-Collin, M.; Centre National de la Recherche Scientifique, 13 - Marseille

    1981-01-01

    In section 2 we describe more carefully the generalized Poisson processes, giving a realization of the underlying probability space, and we characterize these processes by their characteristic functionals. Section 3 is devoted to the proof of the previous formula for quantum mechanical systems, with possibly velocity dependent potentials and in section 4 we give an application of the previous theory to some relativistic Bose field models. (orig.)

  12. On calculations of the ground state energy in quantum mechanics

    International Nuclear Information System (INIS)

    Efimov, G.V.

    1991-02-01

    In nonrelativistic quantum mechanics the Wick-ordering method called the oscillator representation suggested to calculate the ground-state energy for a wide class of potentials allowing the existence of a bound state. The following examples are considered: the orbital excitations of the ground-state in the Coulomb plus linear potential, the Schroedinger equation with a ''relativistic'' kinetic energy √p 2 +m 2 , the Coulomb three-body problem. (author). 22 refs, 2 tabs

  13. Polymer quantum mechanics some examples using path integrals

    International Nuclear Information System (INIS)

    Parra, Lorena; Vergara, J. David

    2014-01-01

    In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems

  14. 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.

  15. Bohm's mechanics. An elementary introduction to the deterministic interpretation of quantum mechanics. 2. enl. and rev. ed.

    International Nuclear Information System (INIS)

    Passon, Oliver

    2010-01-01

    Bohm's mechanics belong to the alternative formulations of quantum mechanics, deviates in their knowledge-theoretical implications however radially from the usual Copenhagen interpretation. Their importance lies by this above all in the region of fundamental questions and the interpretation of quantum mechanics, because they allow yet a solution of the measurement problem discussed since decades controversy. Simultaneously all predictions of usual quantum mechanics can be reproduced. Even though on the German-language textbook market hitherto an elementary introduction to this topic lacked. New in the second edition is a short draft of the relativistic and quantum-field theoretical generalizations.

  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. 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

  18. 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

  19. 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.

  20. 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)

  1. Theory of Thomson scattering in a strong magnetic field, 2. [Relativistic quantum theory, cross sections

    Energy Technology Data Exchange (ETDEWEB)

    Hamada, T [Ibaraki Univ., Mito (Japan). Dept. of Physics

    1975-07-01

    A relativistic quantum theory is formulated for the Compton scattering by electrons in a strong magnetic field. It is shown that the relativistic quantum (Klein-Nishina) cross section in the center of drift system reduces exactly to the classical Thomson cross section in the limit h..omega../2..pi..<quantum number characterizing the energy levels of the electron in the magnetic field. There is one special case for which the Thomson cross section is valid irrespective of the magnitudes of ..omega.. and ..omega..sub(c); the forward scattering in the direction of the magnetic field by an electron in the ground state.

  2. Computational derivation of quantum relativist electromagnetic systems with forward-backward space-time shifts

    International Nuclear Information System (INIS)

    Dubois, Daniel M.

    2000-01-01

    This paper is a continuation of our preceding paper dealing with computational derivation of the Klein-Gordon quantum relativist equation and the Schroedinger quantum equation with forward and backward space-time shifts. The first part introduces forward and backward derivatives for discrete and continuous systems. Generalized complex discrete and continuous derivatives are deduced. The second part deduces the Klein-Gordon equation from the space-time complex continuous derivatives. These derivatives take into account forward-backward space-time shifts related to an internal phase velocity u. The internal group velocity v is related to the speed of light u.v=c 2 and to the external group and phase velocities u.v=v g .v p . Without time shift, the Schroedinger equation is deduced, with a supplementary term, which could represent a reference potential. The third part deduces the Quantum Relativist Klein-Gordon equation for a particle in an electromagnetic field

  3. The microcanonical ensemble of the ideal relativistic quantum gas with angular momentum conservation

    International Nuclear Information System (INIS)

    Becattini, F.; Ferroni, L.

    2007-01-01

    We derive the microcanonical partition function of the ideal relativistic quantum gas with fixed intrinsic angular momentum as an expansion over fixed multiplicities. We developed a group theoretical approach by generalizing known projection techniques to the Poincare group. Our calculation is carried out in a quantum field framework and applies to particles with any spin. It extends known results in the literature in that it does not introduce any large volume approximation, and it takes particle spin fully into account. We provide expressions of the microcanonical partition function at fixed multiplicities in the limiting classical case of large volumes and large angular momenta and in the grand-canonical ensemble. We also derive the microcanonical partition function of the ideal relativistic quantum gas with fixed parity. (orig.)

  4. Quantum theory of relativistic charged particles in external fields

    International Nuclear Information System (INIS)

    Ruijsenaars, S.N.M.

    1976-01-01

    A study was made on external field theories in which the quantized field corresponds to relativistic elementary particles with non-zero rest mass. These particles are assumed to be charged, thus they have distinct antiparticles. The thesis consists of two parts. The first tries to accommodate the general features of theories of relativistic charged particles in external fields. Spin and dynamics in particular are not specified. In the second part, the results are applied to charged spin-1/2 and spin-0 particles, the dynamics of which are given by the Dirac resp. Klein-Gordon equation. The greater emphasis is on external fields which are rapidly decreasing, infinitely differentiable functions of space-time, but also considers time-independent fields. External fields, other than electromagnetic fields are also considered, e.g. scalar fields

  5. 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

  6. On the connections between the classical and quantum-mechanical Kepler problems

    International Nuclear Information System (INIS)

    Dahl, J.P.; Jorgensen, T.G.

    1993-01-01

    The Runge-Lenz vector, which accounts for the accidental degeneracy of the non-relativistic Kepler problem, has been the subject matter of many studies, both in quantum mechanics and in classical mechanics. Much less attention has been paid to the Johnson-Lippmann operator which accounts for the accidental degeneracy of the relativistic Kepler problem in Dirac's quantum-mechanical description. In the present communication we discuss the properties of the Johnson-Lippmann operator. We show its relation to the non-relativistic Runge-Lenz vector and draw a connection to Sommerfield's early discussion of the relativistic Kepler problem. This enables us, inter alia, to give an explanation of the apparent coincidence of the energy expressions of the two theories

  7. Quantum phase space for an ideal relativistic gas in d spatial dimensions

    International Nuclear Information System (INIS)

    Hayashi, M.; Vera Mendoza, H.

    1992-01-01

    We present the closed formula for the d-dimensional invariant phase-space integral for an ideal relativistic gas in an exact integral form. In the particular cases of the nonrelativistic and the extreme relativistic limits the phase-space integrals are calculated analytically. Then we consider the d-dimensional invariant phase space with quantum statistic and derive the cluster decomposition for the grand canonical and canonical partition functions as well as for the microcanonical and grand microcanonical densities of states. As a showcase, we consider the black-body radiation in d dimensions (Author)

  8. 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

  9. 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

  10. 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

  11. 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.

  12. Particle-production mechanism in relativistic heavy-ion collisions

    International Nuclear Information System (INIS)

    Bush, B.W.; Nix, J.R.

    1994-01-01

    We discuss the production of particles in relativistic heavy-ion collisions through the mechanism of massive bremsstrahlung, in which massive mesons are emitted during rapid nucleon acceleration. This mechanism is described within the framework of classical hadrodynamics for extended nucleons, corresponding to nucleons of finite size interacting with massive meson fields. This new theory provides a natural covariant microscopic approach to relativistic heavy-ion collisions that includes automatically spacetime nonlocality and retardation, nonequilibrium phenomena, interactions among all nucleons, and particle production. Inclusion of the finite nucleon size cures the difficulties with preacceleration and runaway solutions that have plagued the classical theory of self-interacting point particles. For the soft reactions that dominate nucleon-nucleon collisions, a significant fraction of the incident center-of-mass energy is radiated through massive bremsstrahlung. In the present version of the theory, this radiated energy is in the form of neutral scalar (σ) and neutral vector (ω) mesons, which subsequently decay primarily into pions with some photons also. Additional meson fields that are known to be important from nucleon-nucleon scattering experiments should be incorporated in the future, in which case the radiated energy would also contain isovector pseudoscalar (π + , π - , π 0 ), isovector scalar (δ + , δ - , δ 0 ), isovector vector (ρ + , ρ - , ρ 0 ), and neutral pseudoscalar (η) mesons

  13. Non-relativistic scalar field on the quantum plane

    International Nuclear Information System (INIS)

    Jahan, A.

    2005-01-01

    We apply the coherent state approach to the non-commutative plane to check the one-loop finiteness of the two-point and four-point functions of a non-relativistic scalar field theory in 2+1 dimensions. We show that the two-point and four-point functions of the model are finite at one-loop level and one recovers the divergent behavior of the model in the limit θ->0 + by appropriate redefinition of the non-commutativity parameter

  14. Quaternionic non abelian relativistic quantum fields in four dimensions

    International Nuclear Information System (INIS)

    Albeverio, S.; Hoeegh-Krohn, R.

    1986-01-01

    We give a simple construction of certain Lie-group valued Euclidean Markov random fields and quantum fields in four dimensions. These fields can be looked upon as non abelian extensions of electromagnetic fields. (orig.)

  15. 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…

  16. Form factor of relativistic two-particle system and covariant hamiltonian formulation of quantum field theory

    International Nuclear Information System (INIS)

    Skachkov, N.; Solovtsov, I.

    1979-01-01

    Based on the hamiltonian formulation of quantum field theory proposed by Kadyshevsky the three-dimensional relativistic approach is developed for describing the form factors of composite systems. The main features of the diagram technique appearing in the covariant hamiltonian formulation of field theory are discussed. The three-dimensional relativistic equation for the vertex function is derived and its connection with that for the quasipotential wave function is found. The expressions are obtained for the form factor of the system through equal-time two-particle wave functions both in momentum and relativistic configurational representations. An explicit expression for the form factor is found for the case of two-particle interaction through the Coulomb potential

  17. Non-relativistic and relativistic quantum kinetic equations in nuclear physics

    International Nuclear Information System (INIS)

    Botermans, W.M.M.

    1989-01-01

    In this thesis an attempt is made to draw up a quantummechanical tranport equation for the explicit calculation oof collision processes between two (heavy) ions, by making proper approaches of the exact equations (non-rel.: N-particles Schroedinger equation; rel.: Euler-Lagrange field equations.). An important starting point in the drag-up of the theory is the behaviour of nuclear matter in equilibrium which is determined by individual as well as collective effects. The central point in this theory is the effective interaction between two nucleons both surrounded by other nucleons. In the derivation of the tranport equations use is made of the green's function formalism as developed by Schwinger and Keldys. For the Green's function kinematic equations are drawn up and are solved by choosing a proper factorization of three- and four-particle Green's functions in terms of one- and two-particle Green's functions. The necessary boundary condition is obtained by explicitly making use of Boltzmann's assumption that colliding particles are statistically uncorrelated. Finally a transport equation is obtained in which the mean field as well as the nucleon-nucleon collisions are given by the same (medium dependent) interaction. This interaction is the non-equilibrium extension of the interaction as given in the Brueckner theory of nuclear matter. Together, kinetic equation and interaction, form a self-consistent set of equations for the case of a non-relativistic as well as for the case of a relativistic starting point. (H.W.) 148 refs.; 6 figs.; 411 schemes

  18. 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.

  19. 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.)

  20. 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)

  1. 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)

  2. 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)

  3. Quantum Statistical Mechanics on a Quantum Computer

    NARCIS (Netherlands)

    Raedt, H. De; Hams, A.H.; Michielsen, K.; Miyashita, S.; Saito, K.; Saito, E.

    2000-01-01

    We describe a simulation method for a quantum spin model of a generic, general purpose quantum computer. The use of this quantum computer simulator is illustrated through several implementations of Grover’s database search algorithm. Some preliminary results on the stability of quantum algorithms

  4. A wave equation interpolating between classical and quantum mechanics

    Science.gov (United States)

    Schleich, W. P.; Greenberger, D. M.; Kobe, D. H.; Scully, M. O.

    2015-10-01

    We derive a ‘master’ wave equation for a family of complex-valued waves {{Φ }}\\equiv R{exp}[{{{i}}S}({cl)}/{{\\hbar }}] whose phase dynamics is dictated by the Hamilton-Jacobi equation for the classical action {S}({cl)}. For a special choice of the dynamics of the amplitude R which eliminates all remnants of classical mechanics associated with {S}({cl)} our wave equation reduces to the Schrödinger equation. In this case the amplitude satisfies a Schrödinger equation analogous to that of a charged particle in an electromagnetic field where the roles of the scalar and the vector potentials are played by the classical energy and the momentum, respectively. In general this amplitude is complex and thereby creates in addition to the classical phase {S}({cl)}/{{\\hbar }} a quantum phase. Classical statistical mechanics, as described by a classical matter wave, follows from our wave equation when we choose the dynamics of the amplitude such that it remains real for all times. Our analysis shows that classical and quantum matter waves are distinguished by two different choices of the dynamics of their amplitudes rather than two values of Planck’s constant. We dedicate this paper to the memory of Richard Lewis Arnowitt—a pioneer of many-body theory, a path finder at the interface of gravity and quantum mechanics, and a true leader in non-relativistic and relativistic quantum field theory.

  5. PREFACE: IARD 2012: 8th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

    Science.gov (United States)

    Horwitz, L. P.; Land, Martin C.; Gill, Tepper; Lusanna, Luca; Salucci, Paolo

    2013-04-01

    Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics. The results of Lindner et al [Physical Review Letters 95 0040401 (2005)] as well as the more recent proposal of Palacios et al [Phys. Rev. Lett. 103 253001 (2009)] and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg [Helv. Phys. Acta 14 322, 588 (1941); 15 23 (1942); see also R P Feynman Phys. Rev. 80 4401 and J S Schwinger Phys. Rev. 82 664 (1951)] could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular

  6. Relativistic quantum channel of communication through field quanta

    International Nuclear Information System (INIS)

    Cliche, M.; Kempf, A.

    2010-01-01

    Setups in which a system Alice emits field quanta that a system Bob receives are prototypical for wireless communication and have been extensively studied. In the most basic setup, Alice and Bob are modeled as Unruh-DeWitt detectors for scalar quanta, and the only noise in their communication is due to quantum fluctuations. For this basic setup, we construct the corresponding information-theoretic quantum channel. We calculate the classical channel capacity as a function of the spacetime separation, and we confirm that the classical as well as the quantum channel capacity are strictly zero for spacelike separations. We show that this channel can be used to entangle Alice and Bob instantaneously. Alice and Bob are shown to extract this entanglement from the vacuum through a Casimir-Polder effect.

  7. The many-body content of quantum gauge theories and its connection to mass generation mechanisms

    International Nuclear Information System (INIS)

    Natoli, C.R.; Palumbo, F.

    1985-01-01

    The aim of the paper is to get more knowledge about many-body systems and their properties, about many-body content of quantum gauge theories and its connection with mass generation mechanisms. The way to achieve this is to perform the galilean limit of the relativistic theory by sending the speed of light c to infinity. This limiting process exposes the low energy behaviour of the relativistic theory

  8. 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.

  9. Optical-lattice Hamiltonians for relativistic quantum electrodynamics

    International Nuclear Information System (INIS)

    Kapit, Eliot; Mueller, Erich

    2011-01-01

    We show how interpenetrating optical lattices containing Bose-Fermi mixtures can be constructed to emulate the thermodynamics of quantum electrodynamics (QED). We present models of neutral atoms on lattices in 1+1, 2+1, and 3+1 dimensions whose low-energy effective action reduces to that of photons coupled to Dirac fermions of the corresponding dimensionality. We give special attention to (2+1)-dimensional quantum electrodynamics (QED3) and discuss how two of its most interesting features, chiral symmetry breaking and Chern-Simons physics, could be observed experimentally.

  10. Estimations for the Schwinger functions of relativistic quantum field theories

    International Nuclear Information System (INIS)

    Mayer, C.D.

    1981-01-01

    Schwinger functions of a relativistic neutral scalar field the basing test function space of which is S or D are estimated by methods of the analytic continuation. Concerning the behaviour in coincident points it is shown: The two-point singularity of the n-point Schwinger function of a field theory is dominated by an inverse power of the distance of both points modulo a multiplicative constant, if the other n-2 points a sufficiently distant and remain fixed. The power thereby, depends only on n. Using additional conditions on the field the independence of the power on n may be proved. Concerning the behaviour at infinite it is shown: The n-point Schwinger functions of a field theory are globally bounded, if the minimal distance of the arguments is positive. The bound depends only on n and the minimal distance of the arguments. (orig.) [de

  11. Quantum dynamics of relativistic bosons through nonminimal vector square potentials

    Energy Technology Data Exchange (ETDEWEB)

    Oliveira, Luiz P. de, E-mail: oliveira.phys@gmail.com

    2016-09-15

    The dynamics of relativistic bosons (scalar and vectorial) through nonminimal vector square (well and barrier) potentials is studied in the Duffin–Kemmer–Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrödinger equations for a component of the DKP spinor. An oscillatory transmission coefficient is found and there is total reflection. Additionally, the energy spectrum of bound states is obtained and reveals the Schiff–Snyder–Weinberg effect, for specific conditions the potential lodges bound states of particles and antiparticles. - Highlights: • DKP bosons in a nonminimal vector square potential are studied. • Spin zero and spin one bosons have the same results. • The Schiff–Snyder–Weinberg effect is observed.

  12. 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.)

  13. Geometric back-reaction in pre-inflation from relativistic quantum geometry

    Energy Technology Data Exchange (ETDEWEB)

    Arcodia, Marcos R.A. [Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), Mar del Plata (Argentina); Bellini, Mauricio [Universidad Nacional de Mar del Plata, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Mar del Plata (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), Mar del Plata (Argentina)

    2016-06-15

    The pre-inflationary evolution of the universe describes the beginning of the expansion from a static initial state, such that the Hubble parameter is initially zero, but increases to an asymptotic constant value, in which it could achieve a de Sitter (inflationary) expansion. The expansion is driven by a background phantom field. The back-reaction effects at this moment should describe vacuum geometrical excitations, which are studied in detail in this work using relativistic quantum geometry. (orig.)

  14. Relativistic quantum dynamics in strong fields: Photon emission from heavy, few-electron ions

    International Nuclear Information System (INIS)

    Fritzsche, S.; Stoehlker, T.

    2005-03-01

    Recent progress in the study of the photon emission from highly-charged heavy ions is reviewed. These investigations show that high-Z ions provide a unique tool for improving the understanding of the electron-electron and electron-photon interaction in the presence of strong fields. Apart from the bound-state transitions, which are accurately described in the framework of quantum electrodynamics, much information has been obtained also from the radiative capture of (quasi-) free electrons by high-Z ions. Many features in the observed spectra hereby confirm the inherently relativistic behavior of even the simplest compound quantum systems in nature. (orig.)

  15. Beyond the hall effect: pratical engineering from relativistic quantum field theory

    International Nuclear Information System (INIS)

    Srivastava, Y.

    1986-01-01

    The author discusses the successful microscopic relativistic quantum field theory viz., quantum electrodynamic (QED) as applied to condensed matter systems. A circuit version of the Heisenberg argument is presented to show that the electric and magnetic flux cannot be measured simultaneously if the usual position/momentum uncertainty of a charged particle confined in a circuit is to be preserved. The author suggests that the electronic transport of a microchip itself obeys some of the same field equations for QED in particular. A comparative list is presented

  16. Time in Quantum Mechanics

    International Nuclear Information System (INIS)

    Reznik, B.

    1999-01-01

    Time plays an unusual role in quantum theory, and the measurement of time is very different from the measurement of other physical qualities associated with a particle. As an example, the measurability of when something occurred is conceptually fraught with difficulties within the theory. Time must be measured by clocks, and one must somehow cause the occurrence of the event of interest to interact with a clock to record when that event occurred. But that interaction carries with it an inevitable perturbation of the event itself. I will argue that in addition to the usual ΔtΔE > ℎ associated with the accuracy of any clock, there is an additional ΔtE > ℎ uncertainty in the measurement of the time of arrival of a particle. Furthermore this constraint arises because the timing device can itself prevent the event from ever occurring at all. I will compare time measurements involving physical clocks, with attempts to construct a time operator and describe new difficulties associated with the latter approach

  17. Irreversibility in quantum mechanics

    International Nuclear Information System (INIS)

    Kadomtsev, Boris B

    2003-01-01

    From the Editorial Board. November 9, 2003 would have marked the seventy-fifth birthday of Boris Borisovich Kadomtsev, were he alive. An outstanding theoretical physicist, teacher, and enlightener, a prominent scientist in plasma physics and controlled nuclear fusion, Kadomtsev was also actively involved in science organization activities. In particular, from 1976 until his untimely death on August 19, 1998, Kadomtsev was the Editor-in-Chief of Physics-Uspekhi, and it is owing to his efforts that the journal improved notably during his tenure. Now, the Editorial Board, with gratitude and sorrow, would like to celebrate his birthday and to honor his blessed memory in these pages. There is, however, a rule - indeed an immutable tradition - in the journal that, except for the Personalia section, no anniversary can be marked in any way other than in a scientific publication. This rule was strictly observed under Kadomtsev, and certainly should not be violated now, even when honoring his memory. Fortunately, there is a video which remained of a lecture on modern problems of quantum physics that Kadomtsev delivered on May 12, 1997. Prepared for publication by M B Kadomtsev, the lecture allows the reader to revisit the heritage of B B Kadomtsev, to appreciate his logic in treating this very difficult area of physics, to hear his voice as it were, to recall Boris Borisovich Kadomtsev and to honor his memory. (methodological notes)

  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. Axioms for nonrelativistic quantum mechanics

    International Nuclear Information System (INIS)

    Guz, W.

    1977-01-01

    On the basis of the axioms assumed it is proved that the logic of propositions concerning any quantum-mechanical system may be endowed with the structure of an orthomodular atomistic complete lattice satisfying the covering postulate, and hence, as a consequence of these axioms, the Piron-MacLaren representation theorem for the logic is obtained. (author)

  20. Renormalization group in quantum mechanics

    International Nuclear Information System (INIS)

    Polony, J.

    1996-01-01

    The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright copyright 1996 Academic Press, Inc

  1. 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.

  2. 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...

  3. Some Mathematical Structures Including Simplified Non-Relativistic Quantum Teleportation Equations and Special Relativity

    International Nuclear Information System (INIS)

    Woesler, Richard

    2007-01-01

    The computations of the present text with non-relativistic quantum teleportation equations and special relativity are totally speculative, physically correct computations can be done using quantum field theory, which remain to be done in future. Proposals for what might be called statistical time loop experiments with, e.g., photon polarization states are described when assuming the simplified non-relativistic quantum teleportation equations and special relativity. However, a closed time loop would usually not occur due to phase incompatibilities of the quantum states. Histories with such phase incompatibilities are called inconsistent ones in the present text, and it is assumed that only consistent histories would occur. This is called an exclusion principle for inconsistent histories, and it would yield that probabilities for certain measurement results change. Extended multiple parallel experiments are proposed to use this statistically for transmission of classical information over distances, and regarding time. Experiments might be testable in near future. However, first a deeper analysis, including quantum field theory, remains to be done in future

  4. Generation of a quantum integrable class of discrete-time or relativistic periodic Toda chains

    International Nuclear Information System (INIS)

    Kundu, Anjan

    1994-01-01

    A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical model close to TC [Lett. Math. Phys. 29 (1993) 165] is presented. All such models are shown to be obtainable from a single ancestor model at different realisations of the underlying quantised algebra. As a consequence the 2x2 Lax operators and the associated quantum R-matrices for these models are easily derived ensuring their quantum integrability. It is shown that the functional Bethe ansatz developed for the quantum TC is trivially generalised to achieve separation of variables also for the present models. ((orig.))

  5. 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

  6. 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

  7. Machine Learning and Quantum Mechanics

    Science.gov (United States)

    Chapline, George

    The author has previously pointed out some similarities between selforganizing neural networks and quantum mechanics. These types of neural networks were originally conceived of as away of emulating the cognitive capabilities of the human brain. Recently extensions of these networks, collectively referred to as deep learning networks, have strengthened the connection between self-organizing neural networks and human cognitive capabilities. In this note we consider whether hardware quantum devices might be useful for emulating neural networks with human-like cognitive capabilities, or alternatively whether implementations of deep learning neural networks using conventional computers might lead to better algorithms for solving the many body Schrodinger equation.

  8. 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.

  9. 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

  10. Quantum Statistical Mechanics on a Quantum Computer

    OpenAIRE

    De Raedt, H.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.

    1999-01-01

    We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.

  11. 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.

  12. 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.

  13. 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

  14. 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)

  15. Anti-hydrogen: The cusp between quantum mechanics and general relativity

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1992-09-01

    We argue that the crossing (CPT) symmetry of relativistic quantum mechanics requires that both the coulombic and the Newtonian force between pairs of particles will reverse when one is replaced by its anti-particle. For consistency, this requires a theory in which both the equivalence principles and gauge invariance are abandoned. thus whether anti-hydrogen ''falls'' up or down will provide an experiment crusis separating general relativity and gauge invariance from this version of quantum mechanics

  16. PREFACE: IARD 2010: The 7th Biennial Conference on Classical and Quantum Relativistic Dynamics of Particles and Fields

    Science.gov (United States)

    Horwitz, Lawrence; Hu, Bei-Lok; Lee, Da-Shin; Gill, Tepper; Land, Martin

    2011-12-01

    Although the subject of relativistic dynamics has been explored from both classical and quantum mechanical points of view since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anamolous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical realtivistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics. The results of Linder et al (Phys. Rev. Lett. 95 0040401 (2005)) as well as the more recent work of Palacios et al (Phys. Rev. Lett. 103 253001 (2009)) and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg (Helv. Phys. Acta 14 322, 588 (1941); 15 23 (1942); see also R P Feynman Phys. Rev. 80 4401 and J S Schwinger Phys. Rev. 82 664 (1951)) could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular, local

  17. 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.

  18. Quantum mechanics of black holes.

    Science.gov (United States)

    Witten, Edward

    2012-08-03

    The popular conception of black holes reflects the behavior of the massive black holes found by astronomers and described by classical general relativity. These objects swallow up whatever comes near and emit nothing. Physicists who have tried to understand the behavior of black holes from a quantum mechanical point of view, however, have arrived at quite a different picture. The difference is analogous to the difference between thermodynamics and statistical mechanics. The thermodynamic description is a good approximation for a macroscopic system, but statistical mechanics describes what one will see if one looks more closely.

  19. 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)

  20. 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

  1. 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

  2. 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

  3. From Quantum Deformations of Relativistic Symmetries to Modified Kinematics and Dynamics

    International Nuclear Information System (INIS)

    Lukierski, J.

    2010-01-01

    We present a short review describing the use of noncommutative spacetime in quantum-deformed dynamical theories: classical and quantum mechanics as well as classical and quantum field theory. We expose the role of Hopf algebras and their realizations (noncommutative modules) as important mathematical tool describing quantum-deformed symmetries: quantum Lie groups and quantum Lie algebras. We consider in some detail the most studied examples of noncommutative space-time geometry: the canonical and κ-deformed cases. Finally, we briefly describe the modifications of Einstein gravity obtained by introduction of noncommutative space-time coordinates. (author)

  4. 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)

  5. Quantum mechanics from general relativity

    International Nuclear Information System (INIS)

    Sachs, M.

    1986-01-01

    A generalization of quantum mechanics is demonstrated in the context of general relativity, following from a generally covariant field theory of inertia. Nonrelativistically, the formalism corresponds with linear quantum mechanics. In the limit of special relativity, nonlinearity remains and several new features are derived: (1) Particle-antiparticle pairs do not annihilate; an exact bound state solution is derived corresponding with all experimental facts about annihilation/creation - which, in approximation, gives the blackbody radiation spectrum for a sea of such pairs. (2) A result is proven, without approximation, that is physically equivalent to the Pauli exclusion principle - which, in linear approximation, gives the totally antisymmetrised many-body wave function and Fermi-Dirac statistics. (3) The hydrogen spectrum is derived, including the Lamb shifts, in agreement with experiment; new results are found for high energy electron-proton scattering. (4) Finally, several applications to the elementary particle domain are demonstrated, in agreement with results from experimental high energy physics. (Auth.)

  6. 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

  7. 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 ?

  8. Substantiating problems of quantum mechanics

    International Nuclear Information System (INIS)

    Gottlieb, J.

    1978-05-01

    Some basic problems, related to the spaces and the operators necessary to describe quantum-mechanical phenomena, are entered upon from a new axiomatic standpoint. Some generalizations are operated, required by convergence criteria, concerning the Fourier transform, the Fourier product and the equation of eigen-values. Physical arguments are brought to support such generalizations and an analysis in view of organizing the structure of the proposed spaces is undertaken. (author)

  9. Supersymmetric quantum mechanics an introduction

    CERN Document Server

    Gangopadhyaya, Asim; Rasinariu, Constantin

    2017-01-01

    We have written this book in order to provide a single compact source for undergraduate and graduate students, as well as for professional physicists who want to understand the essentials of supersymmetric quantum mechanics. It is an outgrowth of a seminar course taught to physics and mathematics juniors and seniors at Loyola University Chicago, and of our own research over a quarter of a century.

  10. Classical and quantum dynamics of a kicked relativistic particle in a box

    Science.gov (United States)

    Yusupov, J. R.; Otajanov, D. M.; Eshniyazov, V. E.; Matrasulov, D. U.

    2018-03-01

    We study classical and quantum dynamics of a kicked relativistic particle confined in a one dimensional box. It is found that in classical case for chaotic motion the average kinetic energy grows in time, while for mixed regime the growth is suppressed. However, in case of regular motion energy fluctuates around certain value. Quantum dynamics is treated by solving the time-dependent Dirac equation with delta-kicking potential, whose exact solution is obtained for single kicking period. In quantum case, depending on the values of the kicking parameters, the average kinetic energy can be quasi periodic, or fluctuating around some value. Particle transport is studied by considering spatio-temporal evolution of the Gaussian wave packet and by analyzing the trembling motion.

  11. Reciprocal relativity of noninertial frames: quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Low, Stephen G [4301 Avenue D, Austin, Texas, 78751 (United States)

    2007-04-06

    Noninertial transformations on time-position-momentum-energy space {l_brace}t, q, p, e{r_brace} with invariant Born-Green metric ds{sup 2} = -dt{sup 2} + 1/c{sup 2} dq{sup 2} + 1/b{sup 2} (dp{sup 2} = 1/c{sup 2} de{sup 2}) and the symplectic metric -de and dt + dp and dq are studied. This U 1,3) group of transformations contains the Lorentz group as the inertial special case and, in the limit of small forces and velocities, reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds{sup 2} -dt{sup 2}. The U(1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. In the limit of b {yields} {infinity}, spacetime is invariant. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary representations of its central extension. The same method of projective representations for the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3) U(1,3) x{sub s} H(4), H(4) is the Weyl-Heisenberg group. The H(4) group, and the associated Heisenberg commutation relations central to quantum mechanics, results directly from requiring projective representations. A set of second-order wave equations result from the representations of the Casimir operators.

  12. 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 ...

  13. On the problem of time in quantum mechanics

    Science.gov (United States)

    Bauer, M.

    2017-05-01

    The problem of time in quantum mechanics (QM) concerns the fact that in the Schrödinger equation time is a parameter, not an operator. Pauli's objection to a time-energy uncertainty relation analogue to the position-momentum one, conjectured by Heisenberg early on, seemed to exclude the existence of such an operator. However Dirac's formulation of an electron's relativistic QM does allow the introduction of a dynamical time operator that is self-adjoint. Consequently, it can be considered as the generator of a unitary transformation of the system, as well as an additional system observable subject to uncertainty. In the present paper these aspects are examined within the standard framework of relativistic QM.

  14. Models of non-relativistic quantum gravity: the good, the bad and the healthy

    CERN Document Server

    Blas, Diego; Sibiryakov, Sergey

    2011-01-01

    Horava's proposal for non-relativistic quantum gravity introduces a preferred time foliation of space-time which violates the local Lorentz invariance. The foliation is encoded in a dynamical scalar field which we call `khronon'. The dynamics of the khronon field is sensitive to the symmetries and other details of the particular implementations of the proposal. In this paper we examine several consistency issues present in three non-relativistic gravity theories: Horava's projectable theory, the healthy non-projectable extension, and a new extension related to ghost condensation. We find that the only model which is free from instabilities and strong coupling is the non-projectable one. We elaborate on the phenomenology of the latter model including a discussion of the couplings of the khronon to matter. In particular, we obtain the parameters of the post-Newtonian expansion in this model and show that they are compatible with current observations.

  15. 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.

  16. 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

  17. A quantum theory of the self-energy of non-relativistic fermions and of the Coulomb-Yukawa force acting between them

    International Nuclear Information System (INIS)

    Ernst, V.

    1978-01-01

    The idea of the systematic Weisskopf-Wigner approximation as used sporadically in atomic physics and quantum optics, is extended here to the interaction of a field of non-relativistic fermions with a field of relativistic bosons. It is shown that the usual (non-existing) interaction Hamiltonian of this system can be written as a sum of a countable number of self-adjoint and bounded partial Hamiltonians. The system of these Hamiltonians defines the order hierarchy of the present approximation scheme. To demonstrate its physical utility it is shown that in a certain order it provides satisfactory quantum theory of the 'self-energy' of the fermions under discussion. This is defined as the binding energy of bosons bound to the fermions and building up the latter's 'individual Coulomb or Yukawa fields' in the sense of expectation values of the corresponding field operator. In states of more than one fermion the bound photons act as a mediating agent between the fermions; this mechanism closely resembles the Coulomb or Yukawa 'forces' used in conventional non-relativistic quantum mechanics. (author)

  18. Quantum information aspects of noncommutative quantum mechanics

    Science.gov (United States)

    Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro

    2018-01-01

    Some fundamental aspects related with the construction of Robertson-Schrödinger-like uncertainty-principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum systems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.

  19. On a two-pass scheme without a faraday mirror for free-space relativistic quantum cryptography

    Energy Technology Data Exchange (ETDEWEB)

    Kravtsov, K. S.; Radchenko, I. V. [Russian Academy of Sciences, Prokhorov General Physics Institute (Russian Federation); Korol' kov, A. V. [Academy of Cryptography (Russian Federation); Kulik, S. P., E-mail: sergei.kulik@gmail.com [Moscow State University (Russian Federation); Molotkov, S. N., E-mail: sergei.molotkov@gmail.com [Academy of Cryptography (Russian Federation)

    2013-05-15

    The stability of destructive interference independent of the input polarization and the state of a quantum communication channel in fiber optic systems used in quantum cryptography plays a principal role in providing the security of communicated keys. A novel optical scheme is proposed that can be used both in relativistic quantum cryptography for communicating keys in open space and for communicating them over fiber optic lines. The scheme ensures stability of destructive interference and admits simple automatic balancing of a fiber interferometer.

  20. On a two-pass scheme without a faraday mirror for free-space relativistic quantum cryptography

    International Nuclear Information System (INIS)

    Kravtsov, K. S.; Radchenko, I. V.; Korol’kov, A. V.; Kulik, S. P.; Molotkov, S. N.

    2013-01-01

    The stability of destructive interference independent of the input polarization and the state of a quantum communication channel in fiber optic systems used in quantum cryptography plays a principal role in providing the security of communicated keys. A novel optical scheme is proposed that can be used both in relativistic quantum cryptography for communicating keys in open space and for communicating them over fiber optic lines. The scheme ensures stability of destructive interference and admits simple automatic balancing of a fiber interferometer.

  1. 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

  2. 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

  3. 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

  4. 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...

  5. 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)

  6. From First Principles: The Application of Quantum Mechanics to Complex Molecules and Solvated Systems

    Energy Technology Data Exchange (ETDEWEB)

    Freitag, Mark A. [Iowa State Univ., Ames, IA (United States)

    2001-12-31

    The major title of this dissertation, 'From first principles,' is a phase often heard in the study of thermodynamics and quantum mechanics. These words embody a powerful idea in the physical sciences; namely, that it is possible to distill the complexities of nature into a set of simple, well defined mathematical laws from which specific relations can then be derived . In thermodynamics, these fundamental laws are immediately familiar to the physical scientist by their numerical order: the First, Second and Third Laws. However, the subject of the present volume is quantum mechanics-specifically, non-relativistic quantum mechanics, which is appropriate for most systems of chemical interest.

  7. 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.

  8. Relativistic atomic matrix elements of rq for arbitrary states in the quantum-defect approximation

    International Nuclear Information System (INIS)

    Owono Owono, L.C.; Owona Angue, M.L.C.; Kwato Njock, M.G.; Oumarou, B.

    2004-01-01

    Recurrence relations used in the calculation of matrix elements of r q for arbitrary q and states of the relativistic one-electron atom with a point-like ionic core are obtained with Dirac and quasirelativistic effective radial Hamiltonians. The phenomenological and supersymmetry-inspired quantum-defect approaches introduced in previous works to model the electron-core interactions are employed. The formulas worked out on the basis of a hypervirial inspired method may be viewed as a generalization to off-diagonal cases of our recently reported results on the evaluation of expectation values of r q

  9. Larmor precession and dwell time of a relativistic particle scattered by a rectangular quantum well

    CERN Document Server

    Li, Z J; Liang, J J; Liang, J Q

    2003-01-01

    The Larmor precession of a relativistic neutral spin particle in a uniform constant magnetic field confined to the region of a one-dimensional rectangular potential well is investigated. The spin precession serves as a clock to measure the time spent by a quantum particle dwelling at a potential well. With the help of a general spin coherent state it is explicitly shown that the spin precession time is equal to the dwell time in the first-order approximation of the infinitesimal field limit. The comparison of the time in a potential well with that in free space shows apparent superluminality.

  10. General-Covariant Quantum Mechanics of Dirac Particle in Curved Space-Times

    International Nuclear Information System (INIS)

    Tagirov, Eh.A.

    1994-01-01

    A general covariant analog of the standard non-relativistic Quantum Mechanics with relativistic corrections in normal geodesic frames in the general Riemannian space-time is constructed for the Dirac particle. Not only the Pauli equation with hermitian Hamiltonian and the pre-Hilbert structure of space of its solutions but also the matrix elements of hermitian operators of momentum, (curvilinear) spatial coordinates and spin of the particle are deduced as general-covariant asymptotic approximation in c -2 , c being the velocity of light, to their naturally determined general-relativistic pre images. It is shown that the Hamiltonian in the Pauli equation originated by the Dirac equation is unitary equivalent to the operator of energy, originated by the metric energy-momentum tensor of the spinor field. Commutation and other properties of the observables connected with the considered change of geometrical background of Quantum Mechanics are briefly discussed. 7 refs

  11. The quantum structure of matter grand challenge project: Large-scale 3-D solutions in relativistic quantum dynamics

    International Nuclear Information System (INIS)

    Wells, J.C.; Oberacker, V.E.; Umar, A.S.

    1993-01-01

    We describe the numerical methods used to solve the time-dependent Dirac equation on a three-dimensional Cartesian lattice. Efficient algorithms are required for computationally intensive studies of nonperturbative relativistic quantum dynamics. Discretization is achieved through the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions on a spatial lattice. All numerical procedures reduce to a series of matrix-vector operations which we perform on the Intel iPSC/860 hypercube, making full use of parallelism. We discuss our solutions to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data stream parallel computers

  12. 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.

  13. 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

  14. Supersymmetric Quantum Mechanics and Topology

    International Nuclear Information System (INIS)

    Wasay, Muhammad Abdul

    2016-01-01

    Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.

  15. Quantum mechanics and umbral calculus

    International Nuclear Information System (INIS)

    Lopez-Sendino, J E; Negro, J; Olmo, M A del; Salgado, E

    2008-01-01

    In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones and the space-time continuous variables by well determined operators that verify some Umbral Calculus conditions. In this way we assure that some properties of integrability and symmetries of the continuous equation are preserved and also the solutions of the continuous case can be recovered discretized in a simple way. The case of the Schroedinger equation with a potential depending only in the space variable is discussed.

  16. Observations on finite quantum mechanics

    International Nuclear Information System (INIS)

    Balian, R.; Itzykson, C.

    1986-01-01

    We study the canonical transformations of the quantum mechanics on a finite phase space. For simplicity we assume that the configuration variable takes an odd prime number 4 K±1 of distinct values. We show that the canonical group is unitarily implemented. It admits a maximal abelian subgroup of order 4 K, commuting with the finite Fourier transform F, a finite analogue of the harmonic oscillator group. This provides a natural construction of F 1/K and of an orthogonal basis of eigenstates of F [fr

  17. Quantum mechanics in phase space

    DEFF Research Database (Denmark)

    Hansen, Frank

    1984-01-01

    A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...

  18. A catastrophe in quantum mechanics

    International Nuclear Information System (INIS)

    Ignatovich, V.K.

    2004-01-01

    The standard scattering theory (SST) in nonrelativistic quantum mechanics (QM) is analyzed. Self-contradictions of SST are deconstructed. A direct way to calculate scattering probability without introduction of a finite volume is discussed. Substantiation of SST in textbooks with the help of wave packets is shown to be incomplete. A complete theory of wave packet scattering on a fixed center is presented, and its similarity to the plane wave scattering is demonstrated. The neutron scattering on a monatomic gas is investigated, and several problems are pointed out. A catastrophic ambiguity of the cross section is revealed, and a way to resolve this ambiguity is discussed

  19. 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

  20. 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.)

  1. 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...

  2. Pion propagator in relativistic quantum field theories of the nuclear many-body problem

    International Nuclear Information System (INIS)

    Matsui, T.; Serot, B.D.

    1982-01-01

    Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models; the scalar-vector theory of Walecka, extended to include π and rho mesons in a non-chiral fashion, and the linear sigma-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pions propagator is evaluated in the one-nucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual NN-bar loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the Lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model Lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored

  3. Simulations of non-relativistic quantum chromodynamics at strong and weak coupling

    Science.gov (United States)

    Shakespeare, Norman Harold

    In this thesis heavy quarks are investigated using lattice nonrelativistic quantum chromodynamics (NRQCD). Two major research works are presented. In the first major work, simulations are done for the three quarkonium systems cc¯, bc¯, and bb¯. The hyperfine splittings are computed at both leading and next-to-leading order in the relativistic expansion, using a large number of lattice spacings. A detailed comparison between mean-link and average plaquette tadpole renormalization schemes is undertaken with a number of features favouring the use of mean-links. These include much better scaling behavior of the hyperfine splittings and smaller relativistic corrections to the spin splittings. Signs of a breakdown in the NRQCD expansion are seen when the bare quark mass, in lattice units, falls below about one. In the second work, coefficients for the perturbative expansion of the static quark self energy are extracted from Monte Carlo simulations in the perturbative region of lattice quantum chromodynamics (QCD). A very large systematic study resulted in a major extension of existing methods. Twisted boundary conditions are used to eliminate the effects of zero modes and to suppress tunneling between the degenerate Z3 vacua. The Monte Carlo results are in excellent agreement with analytic perturbation theory, which is known through second order. New results for the third order coefficient are reported. Preliminary work is reported on quark propagators which will be used to measure second order mass renormalizations for NRQCD fermions.

  4. 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.

  5. Quantum mechanics, relativity and casuality

    International Nuclear Information System (INIS)

    Tati, T.

    1976-01-01

    In quantum mechanics, the state is prepared by a measurement on a spacelike surface sigma. What is that determine the surface sigma on which the measurement prepares the stae. It si considered either a mechanism proper to the measuring process (apparatus) or a universal property of space-time. In the former case, problems arise, concerning casuality or conservation of probability due to the fact that the velocity of reduction of a wave packet is considered to exceed the light velocity. The theory of finite degree of freedom proposed previously belongs to the latter case. In this theory, the surface sigma is restricted to the hyper-plane perpendicular to a universal time-like vector governing casual relations. An experimental to discriminate between the above-mentioned two cases and to test the existence of the universal timelike vector is proposed

  6. Quantum mechanics, relativity and causality

    International Nuclear Information System (INIS)

    Tati, Takao.

    1975-07-01

    In quantum mechanics, the state is prepared by a measurement on a space-like surface sigma. What is that determines the surface sigma on which the measurement prepares the state It is considered either a mechanism proper to the measuring process (apparatus) or a universal property of space-time. In the former case, problems arise, concerning causality or conservation of probability due to that the velocity of reduction of wave-packet is considered to exceed the light velocity. The theory of finite degree of freedom proposed previously belongs to the latter case. In this theory, the surface sigma is restricted to the hyper-plane perpendicular to a universal time-like vector governing causal relations. We propose an experiment to discriminate between the above-mentioned two cases and to test the existence of the universal time-like vector. (auth.)

  7. Contraint's theory and relativistic dynamics

    International Nuclear Information System (INIS)

    Longhi, G.; Lusanna, L.

    1987-01-01

    The purpose of this Workshop was to examine the current situation of relativistic dynamics. In particular, Dirac-Bergmann's theory of constraints, which lies at the heart of gauge theories, general relativity, relativistic mechanics and string theories, was chosen as the unifying theoretical framework best suited to investigate such a field. The papers discussed were on general relativity; relativistic mechanics; particle physics and mathematical physics. Also discussed were the problems of classical and quantum level, namely the identification of the classical observables of constrained systems, the equivalence of the nonequivalence of the various ways to quantize such systems; the problem of the anomalies; the best geometrical approach to the theory of constraints; the possibility of unifying all the treatments of relativistic mechanics. This book compiles the papers presented at proceedings of relativistic dynamics and constraints theory

  8. 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...

  9. 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.)

  10. 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.

  11. The meaning of the wave function in search of the ontology of quantum mechanics

    CERN Document Server

    Gao, Shan

    2017-01-01

    At the heart of quantum mechanics lies the wave function, a powerful but mysterious mathematical object which has been a hot topic of debate from its earliest stages. Covering much of the recent debate and providing a comprehensive and critical review of competing approaches, this ambitious text provides new, decisive proof of the reality of the wave function. Aiming to make sense of the wave function in quantum mechanics and to find the ontological content of the theory, this book explores new ontological interpretations of the wave function in terms of random discontinuous motion of particles. Finally, the book investigates whether the suggested quantum ontology is complete in solving the measurement problem and if it should be revised in the relativistic domain. A timely addition to the literature on the foundations of quantum mechanics, this book is of value to students and researchers with an interest in the philosophy of physics. Presents a concise introduction to quantum mechanics, including the c...

  12. Compatibility conditions of a singular hypersurface in the relativistic mechanics of the continuous media

    International Nuclear Information System (INIS)

    Maugin, G.A.

    1976-01-01

    In this work the compatibility conditions verified by the discontinuities of relativistic fields and of their space-time and time-like derivatives up to be second order are systematically constructed in terms of the local geometry of the wave front (singular hypersurface). A new time-like derivative that generalizes Thomas' delta-derivative of classical continuum mechanics is thus introduced in the relativistic frame. It allows to formulate these conditions in compact forms. It is thus expected that the relativistic analogue of T.Y. Thomas' (1957) classical theory is produced [fr

  13. Quantum mechanics of Proca fields

    International Nuclear Information System (INIS)

    Zamani, Farhad; Mostafazadeh, Ali

    2009-01-01

    We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.

  14. 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...

  15. Quantum tagging: Authenticating location via quantum information and relativistic signaling constraints

    Energy Technology Data Exchange (ETDEWEB)

    Kent, Adrian; Munro, William J.; Spiller, Timothy P. [Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, Cambridge, United Kingdom and Perimeter Institute for Theoretical Physics, Waterloo, Ontario (Canada); NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa 243-0198 (Japan); Quantum Information Science, School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT (United Kingdom)

    2011-07-15

    We define the task of quantum tagging, that is, authenticating the classical location of a classical tagging device by sending and receiving quantum signals from suitably located distant sites, in an environment controlled by an adversary whose quantum information processing and transmitting power is unbounded. We define simple security models for this task and briefly discuss alternatives. We illustrate the pitfalls of naive quantum cryptographic reasoning in this context by describing several protocols which at first sight appear unconditionally secure but which, as we show, can in fact be broken by teleportation-based attacks. We also describe some protocols which cannot be broken by these specific attacks, but do not prove they are unconditionally secure. We review the history of quantum tagging protocols, and show that protocols previously proposed by Malaney and Chandran et al. are provably insecure.

  16. 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)

  17. Quantum relativity theory and quantum space-time

    International Nuclear Information System (INIS)

    Banai, M.

    1984-01-01

    A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis's quantum relativity. The recently proposed classical relativistic quantum theory of Prugovecki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (''elementary particles''). The main new aspect of this quantum mechanics is that it provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that ''quarks'' should be considered as quantum relativistic particles. (author)

  18. 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.

  19. 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

  20. 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.

  1. 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."

  2. Intrinsic periodicity: the forgotten lesson of quantum mechanics

    International Nuclear Information System (INIS)

    Dolce, Donatello

    2013-01-01

    Wave-particle duality, together with the concept of elementary particles, was introduced by de Broglie in terms of intrinsically periodic phenomena. However, after nearly 90 years, the physical origin of such undulatory mechanics remains unrevealed. We propose a natural realization of the de Broglie periodic phenomenon in terms of harmonic vibrational modes associated to space-time periodicities. In this way we find that, similarly to a vibrating string or a particle in a box, the intrinsic recurrence imposed as a constraint to elementary particles represents a fully consistent quantization condition. The resulting cyclic dynamics formally match ordinary relativistic Quantum Mechanics in both the canonical and Feynman formulations. Interactions are introduced in a geometrodynamical way, similarly to general relativity, by simply considering that variations of kinematical state can be equivalently described in terms of modulations of space-time recurrences, as known from undulatory mechanics. We present this novel quantization prescription from an historical prospective.

  3. 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

  4. Reciprocity principle in stochastic quantum mechanics

    International Nuclear Information System (INIS)

    Brooke, J.A.; Guz, W.; Prugovecki, E.

    1982-01-01

    Born's reciprocity theory can be combined with a recently proposed framework for quantum spacetime by requiring that the free test particle propagators obey the Born-Lande equation in addition to the Klein-Gordon equation. If, furthermore, the coordinate transition amplitudes in between various standards are required to be eigenfunctions of Born's metric operator, then a mass formula results which predicts linear dependence on spin of the squared rest mass of elementary particles. This procedure also leads to a guage and reciprocally invariant formulation of the relativistic canonical commutation relations

  5. Note of positions of particles in classical relativistic mechanics

    International Nuclear Information System (INIS)

    Pazma, V.

    1983-01-01

    The relation between world-lines and the position vector of a particle is studied from the point of view of gauge system theory. The expressions for the position vector of a free relativistic particle and of two interacting particles described by the Todorov-Komar model are derived under plausible assumptions. The relation between the physical meaning of basic canonical variables and the choice of a gauge is also discussed. (author)

  6. 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…

  7. 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.

  8. Theoretical investigations in nonlinear quantum optics, theory of measurement, and pulsations of general relativistic models of neutron stars

    International Nuclear Information System (INIS)

    Schumaker, B.L.

    1985-01-01

    This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum-mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and momentum variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes arise from two-proton transitions, i.e., are created or destroyed two at a time. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed. The fifth paper considers the validity of the standard quantum limit (SQL) for measurements that monitor the position of a free mass. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models and of the gravitational waves they emit

  9. 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

  10. 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

  11. Simulations of relativistic quantum plasmas using real-time lattice scalar QED

    Science.gov (United States)

    Shi, Yuan; Xiao, Jianyuan; Qin, Hong; Fisch, Nathaniel J.

    2018-05-01

    Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may be computed using quantum parallelism in the future.

  12. Introduction of a quantum of time ('chronon') and its consequences for quantum mechanics

    International Nuclear Information System (INIS)

    Farias, R.H.A.; Recami, E.; INFN, Milan; Campinas, State University, SP

    1998-01-01

    The authors discuss the consequences of the introduction of a quantum of time τ 0 in the formalism of non-relativistic quantum mechanics, by referring themselves in particular to the theory of the chronon as proposed by P. Caldirola. Such an interesting 'finite difference' theory, forwards -at the classical level- a solution for the motion of a particle endowed with a non-negligible charge in an external electromagnetic field, overcoming all the known difficulties met by Abraham-Lorentz's and Dirac's approaches (and even allowing a clear answer to the question whether a free falling charged particle does or not emit radiation), and -at the quantum level- yields a remarkable mass spectrum for leptons. After having briefly reviewed Caldirola's approach, the first aim of the authors is to work out, discuss, and compare one another the mew representations of Quantum Mechanics (QM) resulting from it, in the Schroedinger, Heisenberg and density-operator (Liouville-von Neumann) pictures, respectively.The authors also obtain the (retarded) finite-difference Schroedinger equation within the Feynman path integral approach, and study some of its relevant solutions. They, then, derive the time-evolution operators of this discrete theory, and use them to get the finite-difference Heisenberg equations. At last, the density matrix formalism is applied to the solution of the measurement problem in QM, with very interesting results, so as a natural explication of 'decoherence', which reveal the power of dicretized (in particular, retarded) QM

  13. Introduction of a quantum of time (`chronon`) and its consequences for quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Farias, R.H.A. [Lab. Nacional de Luz Sincrotron, Campinas, SP (Brazil); Recami, E. [Bergamo Univ. (Italy). Fac. di Ingegneria]|[INFN, Milan (Italy)]|[Campinas, State University, SP (Brazil). DMO-FEEC, CCS

    1998-12-31

    The authors discuss the consequences of the introduction of a quantum of time {tau}{sub 0} in the formalism of non-relativistic quantum mechanics, by referring themselves in particular to the theory of the chronon as proposed by P. Caldirola. Such an interesting `finite difference` theory, forwards -at the classical level- a solution for the motion of a particle endowed with a non-negligible charge in an external electromagnetic field, overcoming all the known difficulties met by Abraham-Lorentz`s and Dirac`s approaches (and even allowing a clear answer to the question whether a free falling charged particle does or not emit radiation), and -at the quantum level- yields a remarkable mass spectrum for leptons. After having briefly reviewed Caldirola`s approach, the first aim of the authors is to work out, discuss, and compare one another the mew representations of Quantum Mechanics (QM) resulting from it, in the Schroedinger, Heisenberg and density-operator (Liouville-von Neumann) pictures, respectively.The authors also obtain the (retarded) finite-difference Schroedinger equation within the Feynman path integral approach, and study some of its relevant solutions. They, then, derive the time-evolution operators of this discrete theory, and use them to get the finite-difference Heisenberg equations. At last, the density matrix formalism is applied to the solution of the measurement problem in QM, with very interesting results, so as a natural explication of `decoherence`, which reveal the power of dicretized (in particular, retarded) QM.

  14. Introduction of a quantum of time (`chronon`) and its consequences for quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Farias, R H.A. [Lab. Nacional de Luz Sincrotron, Campinas, SP (Brazil); Recami, E [Bergamo Univ. (Italy). Fac. di Ingegneria; [INFN, Milan (Italy); [Campinas, State University, SP (Brazil). DMO-FEEC, CCS

    1999-12-31

    The authors discuss the consequences of the introduction of a quantum of time {tau}{sub 0} in the formalism of non-relativistic quantum mechanics, by referring themselves in particular to the theory of the chronon as proposed by P. Caldirola. Such an interesting `finite difference` theory, forwards -at the classical level- a solution for the motion of a particle endowed with a non-negligible charge in an external electromagnetic field, overcoming all the known difficulties met by Abraham-Lorentz`s and Dirac`s approaches (and even allowing a clear answer to the question whether a free falling charged particle does or not emit radiation), and -at the quantum level- yields a remarkable mass spectrum for leptons. After having briefly reviewed Caldirola`s approach, the first aim of the authors is to work out, discuss, and compare one another the mew representations of Quantum Mechanics (QM) resulting from it, in the Schroedinger, Heisenberg and density-operator (Liouville-von Neumann) pictures, respectively.The authors also obtain the (retarded) finite-difference Schroedinger equation within the Feynman path integral approach, and study some of its relevant solutions. They, then, derive the time-evolution operators of this discrete theory, and use them to get the finite-difference Heisenberg equations. At last, the density matrix formalism is applied to the solution of the measurement problem in QM, with very interesting results, so as a natural explication of `decoherence`, which reveal the power of dicretized (in particular, retarded) QM.

  15. Does boundary quantum mechanics imply quantum mechanics in the bulk?

    Science.gov (United States)

    Kabat, Daniel; Lifschytz, Gilad

    2018-03-01

    Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field ϕ (0) as a smeared operator in the CFT. A series of 1 /N corrections must be added to ϕ (0) to represent an interacting bulk field ϕ. These corrections have been determined in the literature from several points of view. Here we develop a new perspective. We show that correlation functions involving ϕ (0) suffer from ambiguities due to analytic continuation. As a result ϕ (0) fails to be a well-defined linear operator in the CFT. This means bulk reconstruction can be understood as a procedure for building up well-defined operators in the CFT which thereby singles out the interacting field ϕ. We further propose that the difficulty with defining ϕ (0) as a linear operator can be re-interpreted as a breakdown of associativity. Presumably ϕ (0) can only be corrected to become an associative operator in perturbation theory. This suggests that quantum mechanics in the bulk is only valid in perturbation theory around a semiclassical bulk geometry.

  16. 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.)

  17. 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

  18. 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)

  19. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    Energy Technology Data Exchange (ETDEWEB)

    Meljanac, Daniel [Ruder Boskovic Institute, Division of Materials Physics, Zagreb (Croatia); Meljanac, Stjepan; Pikutic, Danijel [Ruder Boskovic Institute, Division of Theoretical Physics, Zagreb (Croatia)

    2017-12-15

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincare-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. (orig.)

  20. Particle production and Boltzmann integral form of relativistic quantum transport theory

    International Nuclear Information System (INIS)

    Rafelski, J.; Davis, E.D.; Bialynicki-Birula, I.

    1993-01-01

    The 3+3+1 dimensional relativistic quantum transport equation for the fermion matter field, combines the particle pair production with flow phenomena, which occur at very different time scale. A direct numerical treatment of dynamical situations is therefore practically impossible. The authors attempt a seperation of these two sectors by the method of prediagonalization of the integral equations. They exploit the structure of the resolvent of the transport equations: it contains two poles corresponding to the flow sector and two to the pair production sector. Their hope for practical applications is to treat matter flow as a classical phenomenon and to be able to obtain an integral term describing the pair production accurately

  1. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    International Nuclear Information System (INIS)

    Meljanac, Daniel; Meljanac, Stjepan; Pikutic, Danijel

    2017-01-01

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincare-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. (orig.)

  2. Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

    Science.gov (United States)

    Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel

    2017-12-01

    Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

  3. Polarizabilities of Ba and Ba2: Comparison of molecular beam experiments with relativistic quantum chemistry

    International Nuclear Information System (INIS)

    Schaefer, Sascha; Mehring, Max; Schaefer, Rolf; Schwerdtfeger, Peter

    2007-01-01

    The dielectric response to an inhomogeneous electric field has been investigated for Ba and Ba 2 within a molecular beam experiment. The ratio of the polarizabilities per atom of Ba 2 and Ba is determined to be 1.30±0.13. The experimental result is compared to a high level ab initio quantum chemical coupled cluster calculation with an energy-consistent scalar relativistic small-core pseudopotential for Ba. For the barium atom a polarizability of 40.82 A 3 is obtained and the isotropic value of the polarizability calculated for Ba 2 is 97.88 A 3 , which is in good agreement with the experimental results, demonstrating that a quantitative understanding of the interaction between two closed-shell heavy element metal atoms has been achieved

  4. 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

  5. Influence of light absorption on relativistic self-focusing of Gaussian laser beam in cold quantum plasma

    Science.gov (United States)

    Patil, S. D.; Valkunde, A. T.; Vhanmore, B. D.; Urunkar, T. U.; Gavade, K. M.; Takale, M. V.

    2018-05-01

    When inter particle distance is comparable to the de Broglies wavelength of charged particles, quantum effects in plasmas are unavoidable. We have exploited an influence of light absorption on self-focusing of Gaussian laser beam in cold quantum plasma by considering relativistic nonlinearity. Nonlinear differential equation governing beam-width parameter has been established by using parabolic equation approach under paraxial and WKB approximations. The effect of light absorption on variation of beam-width parameter with dimensionless distance of propagation is presented graphically and discussed. It is found that light absorption plays vital role in weakening the relativistic self-focusing of laser beam during propagation in cold quantum plasma and gives reasonably interesting results.

  6. Density operators in quantum mechanics

    International Nuclear Information System (INIS)

    Burzynski, A.

    1979-01-01

    A brief discussion and resume of density operator formalism in the way it occurs in modern physics (in quantum optics, quantum statistical physics, quantum theory of radiation) is presented. Particularly we emphasize the projection operator method, application of spectral theorems and superoperators formalism in operator Hilbert spaces (Hilbert-Schmidt type). The paper includes an appendix on direct sums and direct products of spaces and operators, and problems of reducibility for operator class by using the projection operators. (author)

  7. 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.)

  8. 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

  9. 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

  10. 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.

  11. 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.

  12. 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.

  13. 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)

  14. 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...

  15. Topological strings from quantum mechanics

    International Nuclear Information System (INIS)

    Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki

    2014-12-01

    We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P 2 , local P 1 x P 1 and local F 1 . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.

  16. Annotations to quantum statistical mechanics

    CERN Document Server

    Kim, In-Gee

    2018-01-01

    This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Baym’s lectures that were presented in the book Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Green’s functions in describing the properties of many-particle systems. The functions provided a method for discussing finite-temperature problems with no more conceptual difficulty than ground-state problems, and the method was equally applicable to boson and fermion systems and equilibrium and nonequilibrium problems. The lectures also explained nonequilibrium statistical physics in a systematic way and contained essential concepts on statistical physics in terms of Green’s functions with sufficient and rigorous details. In-Gee Kim thoroughly studied the lectures during one of his research projects but found that the unspecialized method used to present them in the form of a book reduced their readability. He st...

  17. Bell's inequalities for quantum mechanics

    International Nuclear Information System (INIS)

    Andaas, H.E.

    1991-10-01

    Inequalities corresponding to the generalized Bell's inequalities of local realism are derived for the quantum case. The extremal values permitted by these inequalities exceed those allowed by the generalized Bell's inequalities. Quantum predictions for systems of two spin-1/2 particles prepared as mixtures do not violate Bell's inequalities. 15 refs

  18. 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.

  19. 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)

  20. General-relativistic celestial mechanics. II. Translational equations of motion

    International Nuclear Information System (INIS)

    Damour, T.; Soffel, M.; Xu, C.

    1992-01-01

    The translational laws of motion for gravitationally interacting systems of N arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation [i.e., neglecting terms of order (v/c) 4 in the equations of motion], our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies