Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology

CERN Document Server

Barvinsky, A O

2015-01-01

This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures and the nonperturbative method based on the late time asymptotics of the heat kernel. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter stage of cosmological evolution at an arbitrary value of $\\varLambda$ -- a model of dark energy with its scale played by the dynamical variable that can be fixed by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of gravity theory mediated by a scala...

Euclidean approach to the inflationary universe

International Nuclear Information System (INIS)

Hawking, S.W.

1983-01-01

The aim of this article is to show how the Euclidean approach can be used to study the inflationary universe. Although this formulation may appear counterintuitive in some respects, it has the advantage that it defines a definite quantum state and provides a framework for calculating quantities of interest such as correlation functions or tunnelling probabilities. By contrast, in the more usual approach in real Lorentzian spacetime, it is not so clear what the quantum state should be or how to evaluate such quantities. (author)

Fuzzy Euclidean wormholes in de Sitter space

Energy Technology Data Exchange (ETDEWEB)

Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: r04244003@ntu.edu.tw, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)

2017-07-01

We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.

The real symplectic groups quantum mechanics and optics

International Nuclear Information System (INIS)

Arvind; Mukunda, N.

1995-01-01

We present a utilitarian review of the family of matrix groups Sp(2n,R), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n,R). Global decomposition theorems, interesting subgroups and their generators are described. Turning to n-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and developed a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n,R) action are delineated. (author). 22 refs

Geometric Approach to Quantum Statistical Mechanics and Application to Casimir Energy and Friction Properties

International Nuclear Information System (INIS)

Ichinose, Shoichi

2010-01-01

A geometric approach to general quantum statistical systems (including the harmonic oscillator) is presented. It is applied to Casimir energy and the dissipative system with friction. We regard the (N+1)-dimensional Euclidean coordinate system (X i ,τ) as the quantum statistical system of N quantum (statistical) variables (X τ ) and one Euclidean time variable (t). Introducing paths (lines or hypersurfaces) in this space (X τ ,t), we adopt the path-integral method to quantize the mechanical system. This is a new view of (statistical) quantization of the mechanical system. The system Hamiltonian appears as the area. We show quantization is realized by the minimal area principle in the present geometric approach. When we take a line as the path, the path-integral expressions of the free energy are shown to be the ordinary ones (such as N harmonic oscillators) or their simple variation. When we take a hyper-surface as the path, the system Hamiltonian is given by the area of the hyper-surface which is defined as a closed-string configuration in the bulk space. In this case, the system becomes a O(N) non-linear model. We show the recently-proposed 5 dimensional Casimir energy (ArXiv:0801.3064,0812.1263) is valid. We apply this approach to the visco-elastic system, and present a new method using the path-integral for the calculation of the dissipative properties.

Quantum mechanics as optics on a cylinder of revolution

International Nuclear Information System (INIS)

Malcor, R.

1987-01-01

A pentadimensional wave (4 space dimensions, the interval s of special relativity being added to the space dimension of the ordinary space). The velocity of propagation of this wave is c and its wavelength is the Compton wavelength of the free particle dual to this wave. The corresponding matter wave is nothing else than what the preceding wave exhibits in ordinary space. The L. de Broglie wave length is deduced from Compton's wave length by an operation of intersection. The phase velocity is derived from c by means of the same operation in ordinary space. The speed of the particle is derived from the wave velocity c in the 4-space by an operation of projection. A study is made in details of the case where there is only one coordinate of the ordinary space but most results are valid for 3 dimensions. It is proved that the interval s is equal to the phase of the wave multiplied by the wave of Compton at rest. Many results given by L. de Broglie in his thesis are reinterpreted in the light of this new formalism which have recourse to the new relation E.P.B. operational link between quantum mechanics and special relativity, which is exposed in an Euclidean space instead of a pseudo-Euclidean space. This optics in a space (5-space-time) is nothing else than quantum mechanics of the free particle in ordinary space. The case of the non-free particle can be dealt with, considering variable refraction indices [fr

The positive action conjecture and asymptotically euclidean metrics in quantum gravity

International Nuclear Information System (INIS)

Gibbons, G.W.; Pope, C.N.

1979-01-01

The positive action conjecture requires that the action of any asymptotically Euclidean 4-dimensional Riemannian metric be positive, vanishing if and only if the space is flat. Because any Ricci flat, asymptotically Euclidean metric has zero action and is local extremum of the action which is a local minimum at flat space, the conjecture requires that there are no Ricci flat asymptotically Euclidean metrics other than flat space, which would establish that flat space is the only local minimum. We prove this for metrics on R 4 and a large class of more complicated topologies and for self-dual metrics. We show that if Rsupμsubμ >= 0 there are no bound states of the Dirac equation and discuss the relevance to possible baryon non-conserving processes mediated by gravitational instantons. We conclude that these are forbidden in the lowest stationary phase approximation. We give a detailed discussion of instantons invariant under an SU(2) or SO(3) isometry group. We find all regular solutions, none of which is asymptotically Euclidean and all of which possess a further Killing vector. In an appendix we construct an approximate self-dual metric on K3 - the only simply connected compact manifold which admits a self-dual metric. (orig.) [de

Non-Euclidean spacetime structure and the two-slit experiment

International Nuclear Information System (INIS)

El Naschie, M.S.

2005-01-01

A simple mathematical model for the two-slit experiment is given to account for the wave-particle duality. Subsequently, the various solutions are interpreted via the experimental evidence as a property of the underlying non-Euclidean spacetime topology and geometry at the quantum level

Superintegrability in two-dimensional Euclidean space and associated polynomial solutions

International Nuclear Information System (INIS)

Kalnins, E.G.; Miller, W. Jr; Pogosyan, G.S.

1996-01-01

In this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the spectral functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial base for each of the nonsubgroup base, not just the subgroup cartesian and polar coordinate case, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the N-dimensional isotropic quantum oscillator. 28 refs., 1 tab

Tunneling in expanding Universe: Euclidean and Hamiltonian approaches

International Nuclear Information System (INIS)

Goncharov, A.S.; Linde, A.D.

1986-01-01

The theory of the false vacuum decay in de Sitter space and in the inflationary Universe, and also the theory of the Universe creation ''from nothing'' are discussed. This explained why tunneling in the inflationary Universe differs from that in de Sitter space and cannot be exactly homogeneous. It is shown that in several important cases the Euclidean approach should be considerably modified or is absolutely inapplicable for the description of tunneling in the expanding Universe and of the process of the quantum creation of the Universe. The Hamiltonian approach to the theory of tunneling in expanding Universe is developed. The results obtained by this method are compared with the results obtained by the Euclidean approach

Quantum cosmology

International Nuclear Information System (INIS)

Hawking, S.W.

1984-01-01

The subject of these lectures is quantum effects in cosmology. The author deals first with situations in which the gravitational field can be treated as a classical, unquantized background on which the quantum matter fields propagate. This is the case with inflation at the GUT era. Nevertheless the curvature of spacetime can have important effects on the behaviour of the quantum fields and on the development of long-range correlations. He then turns to the question of the quantization of the gravitational field itself. The plan of these lectures is as follows: Euclidean approach to quantum field theory in flat space; the extension of techniques to quantum fields on a curved background with the four-sphere, the Euclidean version of De Sitter space as a particular example; the GUT era; quantization of the gravitational field by Euclidean path integrals; mini superspace model. (Auth.)

Loop Transfer Matrix and Loop Quantum Mechanics

International Nuclear Information System (INIS)

Savvidy, George K.

2000-01-01

The gonihedric model of random surfaces on a 3d Euclidean lattice has equivalent representation in terms of transfer matrix K(Q i ,Q f ), which describes the propagation of loops Q. We extend the previous construction of the loop transfer matrix to the case of nonzero self-intersection coupling constant κ. We introduce the loop generalization of Fourier transformation which allows to diagonalize transfer matrices, that depend on symmetric difference of loops only and express all eigenvalues of 3d loop transfer matrix through the correlation functions of the corresponding 2d statistical system. The loop Fourier transformation allows to carry out the analogy with quantum mechanics of point particles, to introduce conjugate loop momentum P and to define loop quantum mechanics. We also consider transfer matrix on 4d lattice which describes propagation of memebranes. This transfer matrix can also be diagonalized by using the generalized Fourier transformation, and all its eigenvalues are equal to the correlation functions of the corresponding 3d statistical system. In particular the free energy of the 4d membrane system is equal to the free energy of 3d gonihedric system of loops and is equal to the free energy of 2d Ising model. (author)

Euclidean mirrors: enhanced vacuum decay from reflected instantons

Science.gov (United States)

Akal, Ibrahim; Moortgat-Pick, Gudrid

2018-05-01

We study the tunnelling of virtual matter–antimatter pairs from the quantum vacuum in the presence of a spatially uniform, time-dependent electric background composed of a strong, slow field superimposed with a weak, rapid field. After analytic continuation to Euclidean spacetime, we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production rate. We discuss how important features of two different mechanisms can be analysed and understood via such a rotation in the complex plane. (a) Consistent with previous studies, we first discuss the standard assisted mechanism with a static strong field and certain weak fields with a distinct pole structure in order to show that the reflection takes place exactly at the poles. We also discuss the effect of possible sub-cycle structures. We extend this reflection picture then to weak fields which have no poles present and illustrate the effective reflections with explicit examples. An additional field strength dependence for the rate occurs in such cases. We analytically compute the characteristic threshold for the assisted mechanism given by the critical combined Keldysh parameter. We discuss significant differences between these two types of fields. For various backgrounds, we present the contributing instantons and perform analytical computations for the corresponding rates treating both fields nonperturbatively. (b) In addition, we also study the case with a nonstatic strong field which gives rise to the assisted dynamical mechanism. For different strong field profiles we investigate the impact on the critical combined Keldysh parameter. As an explicit example, we analytically compute the rate by employing the exact reflection points. The validity of the predictions

Variational submanifolds of Euclidean spaces

Science.gov (United States)

Krupka, D.; Urban, Z.; Volná, J.

2018-03-01

Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given non-variational system, conditions assuring variationality (the Helmholtz conditions) of the induced system with respect to a submanifold of a Euclidean space are studied, and the problem of existence of these "variational submanifolds" is formulated in general and solved for second-order systems. The variational sequence theory on sheaves of differential forms is employed as a main tool for the analysis of local and global aspects (variationality and variational triviality). The theory is illustrated by examples of holonomic constraints (submanifolds of a configuration Euclidean space) which are variational submanifolds in geometry and mechanics.

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

Path integrals in quantum mechanics, statistics, polymer physics, and financial markets

CERN Document Server

Kleinert, Hagen

2009-01-01

This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying p

Euclidean fields: vector mesons and photons

International Nuclear Information System (INIS)

Loffelholz, J.

1979-01-01

Free transverse vector fields of mass >= 0 are studied. The model is related to the usual free vector meson and electromagnetic quantum field theories by extension of the field operators from transverse to arbitrary test functions. The one-particle states in transverse gauge and their localization are described. Reflexion positivity is proved and derived are free Feynman-Kac-Nelson formulas. An Euclidean approach to a photon field in a spherical world using dilatation covariance and inversions is given

Classical and quantum integrability of 2D dilaton gravities in Euclidean space

International Nuclear Information System (INIS)

Bergamin, L; Grumiller, D; Kummer, W; Vassilevich, D V

2005-01-01

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a restricted class of topologies is consistent with the metric and the dilaton. A particular case of string motivated Liouville gravity is studied in detail. Path integral quantization in generic Euclidean dilaton gravity is performed non-perturbatively by analogy to the Minkowskian case

From Euclidean to Minkowski space with the Cauchy-Riemann equations

International Nuclear Information System (INIS)

Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.

2008-01-01

We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)

The Euclidean three-point function in loop and perturbative gravity

International Nuclear Information System (INIS)

Rovelli, Carlo; Zhang Mingyi

2011-01-01

We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of γ < 1. We find results consistent with Regge calculus in the limit γ → 0, j → ∞. We also compute the tree-level three-point function of perturbative quantum general relativity in position space and discuss the possibility of directly comparing the two results.

Euclidean mirrors. Enhanced vacuum decay from reflected instantons

Energy Technology Data Exchange (ETDEWEB)

Akal, Ibrahim [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group; Moortgat-Pick, Gudrid [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

2017-06-15

We study the tunneling of virtual matter-antimatter pairs from the quantum vacuum in the presence of a spatially uniform temporal electric background composed of of a strong slow field superimposed with a weak rapid field. After analytic continuation to Euclidean spacetime we obtain from the instanton equations two critical points. While one of them is the closing point of the instanton path, the other serves as an Euclidean mirror which reflects and squeezes the instanton. It is this reflection and shrinking which is responsible for an enormous enhancement of the vacuum pair production rate. We discuss how important features of this mechanism can be analysed and understood via such a rotation in the complex plane. Consistent with previous studies, we consider certain examples where we apply weak fields with a distinct pole structure in order to show that the reflection takes place exactly at the poles. We also discuss the effect of possible sub-cycle structures. We extend this reflection picture to fields which have no poles present and illustrate the effective reflections with explicit examples. An additional field strength dependence for the rate occurs in such cases. We analytically compute the characteristic threshold for this mechanism given by the critical combined Keldysh parameter. We discuss significant differences between these two types of fields. For various backgrounds, we present the contributing instantons and perform analytical computations for the corresponding rates treating both fields nonperturbatively. The validity of the results is confirmed by numerical computations. Considering different profiles for the strong field, we also discuss its impact on the critical combined Keldysh parameter.

Euclidean wormholes with minimally coupled scalar fields

International Nuclear Information System (INIS)

Ruz, Soumendranath; Modak, Bijan; Debnath, Subhra; Sanyal, Abhik Kumar

2013-01-01

A detailed study of quantum and semiclassical Euclidean wormholes for Einstein's theory with a minimally coupled scalar field has been performed for a class of potentials. Massless, constant, massive (quadratic in the scalar field) and inverse (linear) potentials admit the Hawking and Page wormhole boundary condition both in the classically forbidden and allowed regions. An inverse quartic potential has been found to exhibit a semiclassical wormhole configuration. Classical wormholes under a suitable back-reaction leading to a finite radius of the throat, where the strong energy condition is satisfied, have been found for the zero, constant, quadratic and exponential potentials. Treating such classical Euclidean wormholes as an initial condition, a late stage of cosmological evolution has been found to remain unaltered from standard Friedmann cosmology, except for the constant potential which under the back-reaction produces a term like a negative cosmological constant. (paper)

Renormalized G-convolution of n-point functions in quantum field theory. I. The Euclidean case

International Nuclear Information System (INIS)

Bros, Jacques; Manolessou-Grammaticou, Marietta.

1977-01-01

The notion of Feynman amplitude associated with a graph G in perturbative quantum field theory admits a generalized version in which each vertex v of G is associated with a general (non-perturbative) nsub(v)-point function Hsup(nsub(v)), nsub(v) denoting the number of lines which are incident to v in G. In the case where no ultraviolet divergence occurs, this has been performed directly in complex momentum space through Bros-Lassalle's G-convolution procedure. The authors propose a generalization of G-convolution which includes the case when the functions Hsup(nsub(v)) are not integrable at infinity but belong to a suitable class of slowly increasing functions. A finite part of the G-convolution integral is then defined through an algorithm which closely follows Zimmermann's renormalization scheme. The case of Euclidean four-momentum configurations is only treated

A strong coupling simulation of Euclidean quantum gravity

International Nuclear Information System (INIS)

Berg, B.; Hamburg Univ.

1984-12-01

Relying on Regge calculus a systematic numerical investigation of models of 4d Euclidean gravity is proposed. The scale a = 1 0 is set by fixing the expectation value of a length. Possible universality of such models is discussed. The strong coupling limit is defined by taking Planck mass msub(p) -> 0 (in units of 1 0 -1 ). The zero order approximation msub(p) = 0 is called 'fluctuating space' and investigated numerically in two 4d models. Canonical dimensions are realized and both models give a negative expectation value for the scalar curvature density. (orig.)

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

Applications of quantum mechanical techniques to areas outside of quantum mechanics

CERN Document Server

Khrennikov, Andrei

2018-01-01

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

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...

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...

The stochastic versus the Euclidean approach to quantum fields on a static space-time

International Nuclear Information System (INIS)

De Angelis, G.F.; de Falco, D.

1986-01-01

Equations are presented which modify the definition of the Gaussian field in the Rindler chart in order to make contact with the Wightman state, the Hartle-Hawking state, and the Euclidean field. By taking Ornstein-Uhlenbeck processes the authors have chosen, in the sense of stochastic mechanics, to place precisely the Fulling modes in their harmonic oscillator ground state. In this respect, together with the periodicity of Minkowski space-time, the authors observe that the covariance of the Ornstein-Uhlenbeck process can be obtained by analytical continuation of the Wightman function of the harmonic oscillator at zero temperature

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...

The G_Newton --> 0 Limit of Euclidean Quantum Gravity

OpenAIRE

Smolin, Lee

1992-01-01

Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit of Euclidean or complexified general relativity is not a free field theory, but is a theory that describes a linearized self-dual connection propagating on an arbitrary anti-self-dual background. This theory is quantized in the loop representation and, as in the full theory, an infinite dimnensional space of exact solutions to the constraint is found. An inner product is also proposed. The path integral is constructed...

Euclidean supergravity

Science.gov (United States)

de Wit, Bernard; Reys, Valentin

2017-12-01

Supergravity with eight supercharges in a four-dimensional Euclidean space is constructed at the full non-linear level by performing an off-shell time-like reduction of five-dimensional supergravity. The resulting four-dimensional theory is realized off-shell with the Weyl, vector and tensor supermultiplets and a corresponding multiplet calculus. Hypermultiplets are included as well, but they are themselves only realized with on-shell supersymmetry. We also briefly discuss the non-linear supermultiplet. The off-shell reduction leads to a full understanding of the Euclidean theory. A complete multiplet calculus is presented along the lines of the Minkowskian theory. Unlike in Minkowski space, chiral and anti-chiral multiplets are real and supersymmetric actions are generally unbounded from below. Precisely as in the Minkowski case, where one has different formulations of Poincaré supergravity upon introducing different compensating supermultiplets, one can also obtain different versions of Euclidean supergravity.

The imaginary-time path integral and non-time-reversal-invariant saddle points of the Euclidean action

International Nuclear Information System (INIS)

Dasgupta, I.

1998-01-01

We discuss new bounce-like (but non-time-reversal-invariant) solutions to Euclidean equations of motion, which we dub boomerons. In the Euclidean path integral approach to quantum theories, boomerons make an imaginary contribution to the vacuum energy. The fake vacuum instability can be removed by cancelling boomeron contributions against contributions from time reversed boomerons (anti-boomerons). The cancellation rests on a sign choice whose significance is not completely understood in the path integral method. (orig.)

Two-slit experiment: quantum and classical probabilities

International Nuclear Information System (INIS)

Khrennikov, Andrei

2015-01-01

Inter-relation between quantum and classical probability models is one of the most fundamental problems of quantum foundations. Nowadays this problem also plays an important role in quantum technologies, in quantum cryptography and the theory of quantum random generators. In this letter, we compare the viewpoint of Richard Feynman that the behavior of quantum particles cannot be described by classical probability theory with the viewpoint that quantum–classical inter-relation is more complicated (cf, in particular, with the tomographic model of quantum mechanics developed in detail by Vladimir Man'ko). As a basic example, we consider the two-slit experiment, which played a crucial role in quantum foundational debates at the beginning of quantum mechanics (QM). In particular, its analysis led Niels Bohr to the formulation of the principle of complementarity. First, we demonstrate that in complete accordance with Feynman's viewpoint, the probabilities for the two-slit experiment have the non-Kolmogorovian structure, since they violate one of basic laws of classical probability theory, the law of total probability (the heart of the Bayesian analysis). However, then we show that these probabilities can be embedded in a natural way into the classical (Kolmogorov, 1933) probability model. To do this, one has to take into account the randomness of selection of different experimental contexts, the joint consideration of which led Feynman to a conclusion about the non-classicality of quantum probability. We compare this embedding of non-Kolmogorovian quantum probabilities into the Kolmogorov model with well-known embeddings of non-Euclidean geometries into Euclidean space (e.g., the Poincaré disk model for the Lobachvesky plane). (paper)

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).

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

International Nuclear Information System (INIS)

Groeblacher, S.

2010-01-01

This work describes more than four years of research on the effects of the radiation-pressure force of light on macroscopic mechanical structures. The basic system studied here is a mechanical oscillator that is highly reflective and part of an optical resonator. It interacts with the optical cavity mode via the radiation-pressure force. Both the dynamics of the mechanical oscillation and the properties of the light field are modified through this interaction. In our experiments we use quantum optical tools (such as homodyning and down-conversion) with the goal of ultimately showing quantum behavior of the mechanical center of mass motion. In this thesis we present several experiments that pave the way towards this goal and when combined should allow the demonstration of the envisioned quantum phenomena, including entanglement, teleportation and Schroeodinger cat states. The study of quantum behavior of truly macroscopic systems is a long outstanding goal, which will help to answer some of the most fundamental questions in quantum physics today: Why is the world around us classical and not quantum? Is there a size- or mass-limit to systems for them to behave according to quantum mechanics? Is quantum theory complete or do we have to extend it to include mechanisms such as decoherence? Can we use the quantum nature of macroscopic objects to, for example, improve the measurement precision of classical apparatuses? The experiments discussed in this thesis include the very first passive radiation-pressure cooling of a mechanical oscillator in a cryogenic optical resonator, as well as the experimental demonstration of radiation-pressure cooling close to the mechanical quantum ground state. Cooling of the mechanical motion is an important pre-condition for observing quantum effects of the mechanical oscillator. In another experiment, we have demonstrated that we are able to enter the strong-coupling regime of the optomechanical system a regime where coherent energy

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.)

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

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

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...

General Nth order integrals of motion in the Euclidean plane

International Nuclear Information System (INIS)

Post, S; Winternitz, P

2015-01-01

The general form of an integral of motion that is a polynomial of order N in the momenta is presented for a Hamiltonian system in two-dimensional Euclidean space. The classical and the quantum cases are treated separately, emphasizing both the similarities and the differences between the two. The main application will be to study Nth order superintegrable systems that allow separation of variables in the Hamilton–Jacobi and Schrödinger equations, respectively. (paper)

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)

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.

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

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.

Constraint algebra in Smolin's G →0 limit of 4D Euclidean gravity

Science.gov (United States)

Varadarajan, Madhavan

2018-05-01

Smolin's generally covariant GNewton→0 limit of 4d Euclidean gravity is a useful toy model for the study of the constraint algebra in loop quantum gravity (LQG). In particular, the commutator between its Hamiltonian constraints has a metric dependent structure function. While a prior LQG-like construction of nontrivial anomaly free constraint commutators for the model exists, that work suffers from two defects. First, Smolin's remarks on the inability of the quantum dynamics to generate propagation effects apply. Second, the construction only yields the action of a single Hamiltonian constraint together with the action of its commutator through a continuum limit of corresponding discrete approximants; the continuum limit of a product of two or more constraints does not exist. Here, we incorporate changes in the quantum dynamics through structural modifications in the choice of discrete approximants to the quantum Hamiltonian constraint. The new structure is motivated by that responsible for propagation in an LQG-like quantization of paramatrized field theory and significantly alters the space of physical states. We study the off shell constraint algebra of the model in the context of these structural changes and show that the continuum limit action of multiple products of Hamiltonian constraints is (a) supported on an appropriate domain of states, (b) yields anomaly free commutators between pairs of Hamiltonian constraints, and (c) is diffeomorphism covariant. Many of our considerations seem robust enough to be applied to the setting of 4d Euclidean gravity.

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.

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

Non-euclidean simplex optimization

International Nuclear Information System (INIS)

Silver, G.L.

1977-01-01

Geometric optimization techniques useful for studying chemical equilibrium traditionally rely upon principles of euclidean geometry, but such algorithms may also be based upon principles of a non-euclidean geometry. The sequential simplex method is adapted to the hyperbolic plane, and application of optimization to problems such as the potentiometric titration of plutonium is suggested

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.)

Spacetime and Euclidean geometry

Science.gov (United States)

Brill, Dieter; Jacobson, Ted

2006-04-01

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.

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...

Matrix quantum mechanics on S1/Z2

Directory of Open Access Journals (Sweden)

P. Betzios

2018-03-01

Full Text Available We study Matrix Quantum Mechanics on the Euclidean time orbifold S1/Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

Matrix quantum mechanics on S1 /Z2

Science.gov (United States)

Betzios, P.; Gürsoy, U.; Papadoulaki, O.

2018-03-01

We study Matrix Quantum Mechanics on the Euclidean time orbifold S1 /Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

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

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.

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

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.

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.

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

International Nuclear Information System (INIS)

Whitaker, A

2004-01-01

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

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.

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.)

Euclidean Monte Carlo simulation of nuclear interactions

International Nuclear Information System (INIS)

Montvay, Istvan; Bonn Univ.; Urbach, Carsten

2011-05-01

We present an exploratory study of chiral effective theories of nuclei with methods adopted from lattice quantum chromodynamics (QCD). We show that the simulations in the Euclidean path integral approach are feasible and that we can determine the energy of the two nucleon state. By varying the parameters and the simulated volumes phase shifts can be determined in principle and hopefully tuned to their physical values in the future. The physical cut-off of the theory is realised by blocking of the lattice fields. By keeping this physical cut-off fixed in physical units the lattice cut-off can be changed and in this way the lattice artefacts can be eliminated. (orig.)

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.

Theory of interacting quantum fields

International Nuclear Information System (INIS)

Rebenko, Alexei L.

2012-01-01

This monograph is devoted to the systematic presentation of foundations of the quantum field theory. Unlike numerous monographs devoted to this topic, a wide range of problems covered in this book are accompanied by their sufficiently clear interpretations and applications. An important significant feature of this monograph is the desire of the author to present mathematical problems of the quantum field theory with regard to new methods of the constructive and Euclidean field theory that appeared in the last thirty years of the 20 th century and are based on the rigorous mathematical apparatus of functional analysis, the theory of operators, and the theory of generalized functions. The monograph is useful for students, post-graduate students, and young scientists who desire to understand not only the formality of construction of the quantum field theory but also its essence and connection with the classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of path integral formalism.

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.)

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

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

Extended supersymmetry in four-dimensional Euclidean space

International Nuclear Information System (INIS)

McKeon, D.G.C.; Sherry, T.N.

2000-01-01

Since the generators of the two SU(2) groups which comprise SO(4) are not Hermitian conjugates of each other, the simplest supersymmetry algebra in four-dimensional Euclidean space more closely resembles the N=2 than the N=1 supersymmetry algebra in four-dimensional Minkowski space. An extended supersymmetry algebra in four-dimensional Euclidean space is considered in this paper; its structure resembles that of N=4 supersymmetry in four-dimensional Minkowski space. The relationship of this algebra to the algebra found by dimensionally reducing the N=1 supersymmetry algebra in ten-dimensional Euclidean space to four-dimensional Euclidean space is examined. The dimensional reduction of N=1 super Yang-Mills theory in ten-dimensional Minkowski space to four-dimensional Euclidean space is also considered

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.

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

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...

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

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.)

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...

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.))

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...

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

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.)

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.)

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.)

Ideas of space. Euclidean, non-Euclidean and relativistic

Energy Technology Data Exchange (ETDEWEB)

Gray, J

1979-01-01

An historical and chronological account of mathematics is presented in which familiarity with simple equations and elements of trigonometry is needed but no specialist knowledge is assumed although difficult problems are discussed. By discussion of the difficulties and confusions it is hoped to understand mathematics as a dynamic activity. Beginning with early Greek mathematics, the Eastern legacy and the transition to deductive and geometric thinking the problem of parallels is then encountered and discussed. The second part of the book takes the story from Wallis, Saccheri and Lambert through to its resolution by Gauss, Lobachevskii, Bolyai, Riemann and Bettrami. The background of the 19th century theory of surfaces is given. The third part gives an account of Einstein's theories based on what has gone before, moving from a Newtonian-Euclidean picture to an Einsteinian-nonEuclidean one. A brief account of gravitation, the nature of space and black holes concludes the book.

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.

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

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...

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

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

Fast Exact Euclidean Distance (FEED) Transformation

NARCIS (Netherlands)

Schouten, Theo; Kittler, J.; van den Broek, Egon; Petrou, M.; Nixon, M.

2004-01-01

Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number

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

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.

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

On construction of two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space

International Nuclear Information System (INIS)

Saveliev, M.V.

1983-01-01

In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)

A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime

Science.gov (United States)

Sciarretta, Antonio

2018-01-01

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum, as well as momentum entanglement.

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.

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

Fixed points of quantum gravity

OpenAIRE

Litim, D F

2003-01-01

Euclidean quantum gravity is studied with renormalisation group methods. Analytical results for a non-trivial ultraviolet fixed point are found for arbitrary dimensions and gauge fixing parameter in the Einstein-Hilbert truncation. Implications for quantum gravity in four dimensions are discussed.

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

Minimal Paths in the City Block: Human Performance on Euclidean and Non-Euclidean Traveling Salesperson Problems

Science.gov (United States)

Walwyn, Amy L.; Navarro, Daniel J.

2010-01-01

An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…

SLE as a Mating of Trees in Euclidean Geometry

Science.gov (United States)

Holden, Nina; Sun, Xin

2018-05-01

The mating of trees approach to Schramm-Loewner evolution (SLE) in the random geometry of Liouville quantum gravity (LQG) has been recently developed by Duplantier et al. (Liouville quantum gravity as a mating of trees, 2014. arXiv:1409.7055). In this paper we consider the mating of trees approach to SLE in Euclidean geometry. Let {η} be a whole-plane space-filling SLE with parameter {κ > 4} , parameterized by Lebesgue measure. The main observable in the mating of trees approach is the contour function, a two-dimensional continuous process describing the evolution of the Minkowski content of the left and right frontier of {η} . We prove regularity properties of the contour function and show that (as in the LQG case) it encodes all the information about the curve {η} . We also prove that the uniform spanning tree on {Z^2} converges to SLE8 in the natural topology associated with the mating of trees approach.

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

Exact Boson-Fermion Duality on a 3D Euclidean Lattice

Science.gov (United States)

Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao; Raghu, S.

2018-01-01

The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.

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.)

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

Science.gov (United States)

Cataloglu, Erdat

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

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.)

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

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).

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.

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

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

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.

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...

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

Quantum mechanics and quantum information a guide through the quantum world

CERN Document Server

Fayngold, Moses

2013-01-01

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

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

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.)

Statistical approach to quantum field theory. An introduction

International Nuclear Information System (INIS)

Wipf, Andreas

2013-01-01

Based on course-tested notes and pedagogical in style. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Authored by a leading researcher in the field. Contains end-of-chapter problems and listings of short, useful computer programs. Contains end-of-chapter problems and listings of short, useful computer programs. Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an ''experimental'' tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate students and, as

Modular groups in quantum field theory

International Nuclear Information System (INIS)

Borchers, H.-J.

2000-01-01

The author discusses the connection of Lagrangean quantum field theory, perturbation theory, the Lehmann-Symanzik-Zimmermann theory, Wightman's quantum field theory, the Euclidean quantum field theory, and the Araki-Haag-Kastler theory of local observables with modular groups. In this connection he considers the PCT-theorem, and the tensor product decomposition. (HSI)

Quantum cosmology of a conformal multiverse

Science.gov (United States)

Robles-Pérez, Salvador J.

2017-09-01

This paper studies the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of universes, and all of them are periodically distributed along the complex time axis. From a classical point of view, they are then isolated, separated by Euclidean regions that represent quantum mechanical barriers. Quantum mechanically, however, there is a nonzero probability for the state of the universes to tunnel out through a Euclidean instanton and suffer a sudden transition to another state of the spacetime. We compute the probability of transition for this and other nonlocal processes like the creation of universes in entangled pairs and, generally speaking, in multipartite entangled states. We obtain the quantum state of a single universe within the formalism of the Wheeler-DeWitt equation and give the semiclassical state of the universes that describes the quantum mechanics of a scalar field propagating in a de Sitter background spacetime. We show that the superposition principle of the quantum mechanics of matter fields alone is an emergent feature of the semiclassical description of the universe that is not valid, for instance, in the spacetime foam. We use the third quantization formalism to describe the creation of an entangled pair of universes with opposite signs of the momentum conjugated to the scale factor. Each universe of the entangled pair represents an expanding spacetime in terms of the Wentzel-Kramers-Brillouin (WKB) time experienced by internal observers in their particle physics experiments. We compute the effective value of the Friedmann equation of the background spacetime of the two entangled universes, and thus, the effect that the entanglement would have in their expansion rates. We analyze as well the effects of the interuniversal entanglement in the properties of the scalar fields that propagate in each

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...

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)

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

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.)

Euclidean supersymmetry, twisting and topological sigma models

International Nuclear Information System (INIS)

Hull, C.M.; Lindstroem, U.; Santos, L. Melo dos; Zabzine, M.; Unge, R. von

2008-01-01

We discuss two dimensional N-extended supersymmetry in Euclidean signature and its R-symmetry. For N = 2, the R-symmetry is SO(2) x SO(1, 1), so that only an A-twist is possible. To formulate a B-twist, or to construct Euclidean N = 2 models with H-flux so that the target geometry is generalised Kahler, it is necessary to work with a complexification of the sigma models. These issues are related to the obstructions to the existence of non-trivial twisted chiral superfields in Euclidean superspace.

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.

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.

Macroscopic quantum tunneling in a dc SQUID

International Nuclear Information System (INIS)

Chen, Y.C.

1986-01-01

The theory of macroscopic quantum tunneling is applied to a current-biased dc SQUID whose dynamics can be described by a two-dimensional mechanical system with a dissipative environment. Based on the phenomenological model proposed by Caldeira and Leggett, the dissipative environment is represented by a set of harmonic oscillators coupling to the system. After integrating out the environmental degrees of freedom, an effective Euclidean action is found for the two-dimensional system. The action is used to provide the quantum tunneling rate formalism for the dc SQUID. Under certain conditions, the tunneling rate reduces to that of a single current-biased Josephson junction with an adjustable effective critical current

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.

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.)

Emerging interpretations of quantum mechanics and recent progress in quantum measurement

International Nuclear Information System (INIS)

Clarke, M L

2014-01-01

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

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.

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.

Is quantum gravity unpredictable

International Nuclear Information System (INIS)

Gross, D.J.

1984-01-01

An investigation of Hawking's proposal that the inclusion of topologically non-trivial manifolds in the functional integral of quantum gravity leads to the loss of quantum coherence is carried out. We discuss some of the problems associated with Hawking's Dollar-matrix theory, including the breakdown of the connection between symmetry principles and conservation laws. It is proposed to use Kaluza-Klein theories to study this issue, since these theories contain well-defined euclidean instantons. These can be used to perform explicit semiclassical calculations of the effects of space-time foam. A general method is presented for constructing Kaluza-Klein instantons based on solutions of ordinary Yang-Mills theory. It is argued that none of these will lead to a breakdown of quantum mechanics. The physical effects of space-time foam are discussed in some detail using explicit instantons of a four-dimensional Kaluza-Klein theory. (orig.)

A linear-time algorithm for Euclidean feature transform sets

NARCIS (Netherlands)

Hesselink, Wim H.

2007-01-01

The Euclidean distance transform of a binary image is the function that assigns to every pixel the Euclidean distance to the background. The Euclidean feature transform is the function that assigns to every pixel the set of background pixels with this distance. We present an algorithm to compute the

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...

Progress in post-quantum mechanics

Science.gov (United States)

Sarfatti, Jack

2017-05-01

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

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

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...

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…

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

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

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)

Triviality - quantum decoherence of Fermionic quantum chromodynamics SU (Nc) in the presence of an external strong U (∞) flavored constant noise field

International Nuclear Information System (INIS)

Botelho, Luiz C.L.

2008-01-01

We analyze the triviality-quantum decoherence of Euclidean quantum chromodynamics in the gauge invariant quark current sector in the presence of an external U (∞) flavor constant charged white noise reservoir. (author)

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.)

Founding Gravitation in 4D Euclidean Space-Time Geometry

International Nuclear Information System (INIS)

Winkler, Franz-Guenter

2010-01-01

The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this view involves variations of the speed of light (depending on location and direction) and a Euclidean principle of general covariance. In this article, a gravitation model by Jan Broekaert, which implements a view of relativity theory in the spirit of Lorentz and Poincare, is reconstructed and shown to fulfill the principles of the Euclidean approach after an appropriate reinterpretation.

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

International Nuclear Information System (INIS)

Smolin, L.

1984-01-01

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

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)

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.

Constructive curves in non-Euclidean planes

OpenAIRE

Horváth, Ákos G.

2016-01-01

In this paper we overview the theory of conics and roulettes in four non-Euclidean planes. We collect the literature about these classical concepts, from the eighteenth century to the present, including papers available only on arXiv. The comparison of the four non-Euclidean planes, in terms of the known results on conics and roulettes, reflects only the very subjective view of the author.

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

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.

Entropy, extremality, euclidean variations, and the equations of motion

Science.gov (United States)

Dong, Xi; Lewkowycz, Aitor

2018-01-01

We study the Euclidean gravitational path integral computing the Rényi entropy and analyze its behavior under small variations. We argue that, in Einstein gravity, the extremality condition can be understood from the variational principle at the level of the action, without having to solve explicitly the equations of motion. This set-up is then generalized to arbitrary theories of gravity, where we show that the respective entanglement entropy functional needs to be extremized. We also extend this result to all orders in Newton's constant G N , providing a derivation of quantum extremality. Understanding quantum extremality for mixtures of states provides a generalization of the dual of the boundary modular Hamiltonian which is given by the bulk modular Hamiltonian plus the area operator, evaluated on the so-called modular extremal surface. This gives a bulk prescription for computing the relative entropies to all orders in G N . We also comment on how these ideas can be used to derive an integrated version of the equations of motion, linearized around arbitrary states.

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

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

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.

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 ...

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

International Nuclear Information System (INIS)

Plotnitsky, Arkady

2014-01-01

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

Spinors in euclidean field theory, complex structures and discrete symmetries

International Nuclear Information System (INIS)

Wetterich, C.

2011-01-01

We discuss fermions for arbitrary dimensions and signature of the metric, with special emphasis on euclidean space. Generalized Majorana spinors are defined for d=2,3,4,8,9mod8, independently of the signature. These objects permit a consistent analytic continuation of Majorana spinors in Minkowski space to euclidean signature. Compatibility of charge conjugation with complex conjugation requires for euclidean signature a new complex structure which involves a reflection in euclidean time. The possible complex structures for Minkowski and euclidean signature can be understood in terms of a modulo two periodicity in the signature. The concepts of a real action and hermitean observables depend on the choice of the complex structure. For a real action the expectation values of all hermitean multi-fermion observables are real. This holds for arbitrary signature, including euclidean space. In particular, a chemical potential is compatible with a real action for the euclidean theory. We also discuss the discrete symmetries of parity, time reversal and charge conjugation for arbitrary dimension and signature.

Euclidean distance degrees of real algebraic groups

NARCIS (Netherlands)

Baaijens, J.A.; Draisma, J.

2015-01-01

We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the new results that we prove is a formula for the Euclidean

Euclidean distance degrees of real algebraic groups

NARCIS (Netherlands)

Baaijens, J.A.; Draisma, J.

2014-01-01

We study the problem of finding, in a real algebraic matrix group, the matrix closest to a given data matrix. We do so from the algebro-geometric perspective of Euclidean distance degrees. We recover several classical results; and among the new results that we prove is a formula for the Euclidean

Topics in string theory and quantum gravity

CERN Document Server

Alvarez-Gaume, Luis

1992-01-01

These are the lecture notes for the Les Houches Summer School on Quantum Gravity held in July 1992. The notes present some general critical assessment of other (non-string) approaches to quantum gravity, and a selected set of topics concerning what we have learned so far about the subject from string theory. Since these lectures are long (133 A4 pages), we include in this abstract the table of contents, which should help the user of the bulletin board in deciding whether to latex and print the full file. 1-FIELD THEORETICAL APPROACH TO QUANTUM GRAVITY: Linearized gravity; Supergravity; Kaluza-Klein theories; Quantum field theory and classical gravity; Euclidean approach to Quantum Gravity; Canonical quantization of gravity; Gravitational Instantons. 2-CONSISTENCY CONDITIONS: ANOMALIES: Generalities about anomalies; Spinors in 2n dimensions; When can we expect to find anomalies?; The Atiyah-Singer Index Theorem and the computation of anomalies; Examples: Green-Schwarz cancellation mechanism and Witten's SU(2) ...

Quantum mechanics

CERN Document Server

Rae, Alastair I M

2007-01-01

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

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

Quantum-mechanical computers and uncomputability

International Nuclear Information System (INIS)

Lloyd, S.

1993-01-01

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

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

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.)

Non-euclidean geometry

CERN Document Server

Coxeter, HSM

1965-01-01

This textbook introduces non-Euclidean geometry, and the third edition adds a new chapter, including a description of the two families of 'mid-lines' between two given lines and an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, and other new material.

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

Quantum Gravity, Dynamical Triangulation and Higer Derivative Regularization

DEFF Research Database (Denmark)

Ambjorn, J.; Jurkiewicz, J.; Kristjansen, C. F.

1992-01-01

We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the bare coupling constants is studied in the search for a sens......We consider a discrete model of euclidean quantum gravity in four dimensions based on a summation over random simplicial manifolds. The action used is the Einstein-Hilbert action plus an $R^2$-term. The phase diagram as a function of the bare coupling constants is studied in the search...

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

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.

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.)

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...

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

International Nuclear Information System (INIS)

Yang, C.-D.

2006-01-01

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

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

International Nuclear Information System (INIS)

Mugur-Schaechter, M.

1993-01-01

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

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

Moessbauer neutrinos in quantum mechanics and quantum field theory

International Nuclear Information System (INIS)

Kopp, Joachim

2009-01-01

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

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.

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

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.

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.)

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

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.

Implementing quantum Ricci curvature

Science.gov (United States)

Klitgaard, N.; Loll, R.

2018-05-01

Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are scalability, computability, and robustness. We demonstrate that these properties continue to hold in the context of nonperturbative quantum gravity, by evaluating the quantum Ricci curvature numerically in two-dimensional Euclidean quantum gravity, defined in terms of dynamical triangulations. Despite the well-known, highly nonclassical properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.

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), ...

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.

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.

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.

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

Quantum mechanics and stochastic mechanics for compatible observables at different times

International Nuclear Information System (INIS)

Correggi, M.; Morchio, G.

2002-01-01

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

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

Triviality-quantum decoherence of quantum chromodynamics SU(∞) in the presence of an external strong white-noise electromagnetic field

International Nuclear Information System (INIS)

Botelho, Luiz C.L.

2004-01-01

We analyze the triviality-quantum decoherence of Euclidean quantum chromodynamics in the gauge invariant quark current sector in the presence of a very strong external white-noise electromagnetic (strength) field within the context of QCD in the 't Hooft limit of a large number of colors

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

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

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 ...

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 ...

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.

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.

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.

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.

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

Quantum Cosmology

OpenAIRE

Page, Don N.

2006-01-01

A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum cosmology, item (2) is the quantum state of the cosmos. Hartle and Hawking have made the `no-boundary' proposal, that the wavefunction of the universe is given by a path integral over all compact Euclidean 4-dimensional geometries and matter fields that hav...

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

International Nuclear Information System (INIS)

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

2004-01-01

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

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

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.

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)

Undergraduate quantum mechanics: lost opportunities for engaging motivated students?

Science.gov (United States)

Johansson, Anders

2018-03-01

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

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.

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)

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.

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.

Chaos. Possible underpinnings for quantum mechanics?

International Nuclear Information System (INIS)

McHarris, Wm.C.

2004-01-01

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

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.

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

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.

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.

Quantum mechanics as total physical theory

International Nuclear Information System (INIS)

Slavnov, D.A.

2002-01-01

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

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

Quantum mechanics in coherent algebras on phase space

International Nuclear Information System (INIS)

Lesche, B.; Seligman, T.H.

1986-01-01

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

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

International Nuclear Information System (INIS)

Greiner, W.

2005-01-01

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

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...

Macroscopic quantum mechanics: theory and experimental concepts of optomechanics

International Nuclear Information System (INIS)

Chen Yanbei

2013-01-01

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

Supersymmetric quantum mechanics on n-dimensional manifolds

International Nuclear Information System (INIS)

O'Connor, M.

1990-01-01

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

The mechanism of suppression of quantum transitions (quantum whirligig)

International Nuclear Information System (INIS)

Buts, V.A.

2010-01-01

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

Generalized inequalities for quantum correlations with hidden variables

International Nuclear Information System (INIS)

Vinduska, M.

1991-01-01

Renowned inequalities for quantum correlations are generalized for the case when quantum system cannot be described with an absolute independent measure of the probability. Such a formulation appears to be suitable for the formulation of the hidden variables theory in terms of non-Euclidean geometry. 10 refs

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.

Absence of even-integer ζ-function values in Euclidean physical quantities in QCD

Science.gov (United States)

Jamin, Matthias; Miravitllas, Ramon

2018-04-01

At order αs4 in perturbative quantum chromodynamics, even-integer ζ-function values are present in Euclidean physical correlation functions like the scalar quark correlation function or the scalar gluonium correlator. We demonstrate that these contributions cancel when the perturbative expansion is expressed in terms of the so-called C-scheme coupling αˆs which has recently been introduced in Ref. [1]. It is furthermore conjectured that a ζ4 term should arise in the Adler function at order αs5 in the MS ‾-scheme, and that this term is expected to disappear in the C-scheme as well.

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

Science.gov (United States)

Aspelmeyer, Markus; Schwab, Keith

2008-09-01

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

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�...

Particle creation and destruction of quantum coherence by topological change

International Nuclear Information System (INIS)

Lavrelashvili, G.V.; Rubakov, V.A.; Tinyakov, P.G.

1988-01-01

The possibility is considered that changes of spatial topology occur as tunneling events in quantum gravity. Creation of scalar and spinor particles during these tunneling transitions is studied. The relevant formalism based on the euclidean Schroedinger equation and coherent state representation is developed. This formalism is illustrated in a two-dimensional example. It is argued that the particle creation during the topological changes induces the loss of quantum coherence. The particle creation is calculated in the case of O(4)-invariant background euclidean four-dimensional metrics. This calculation is used for estimating the loss of quantum coherence. An upper limit on the rate of the topological changes, A -17 M 4 Pl , is derived from the observation of K 0 -anti K 0 oscillations. (orig.)

Euclidean and Lorentzian Quantum Gravity – Lessons from Two Dimensions

NARCIS (Netherlands)

Ambjørn, J.; Loll, R.; Nielsen, J. L.; Rolf, J.

1998-01-01

No theory of four-dimensional quantum gravity exists as yet. In this situation the two-dimensional theory, which can be analyzed by conventional field-theoretical methods, can serve as a toy model for studying some aspects of quantum gravity. It represents one of the rare settings in a

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...

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...

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

Fixed-topology Lorentzian triangulations: Quantum Regge Calculus in the Lorentzian domain

Science.gov (United States)

Tate, Kyle; Visser, Matt

2011-11-01

A key insight used in developing the theory of Causal Dynamical Triangu-lations (CDTs) is to use the causal (or light-cone) structure of Lorentzian manifolds to restrict the class of geometries appearing in the Quantum Gravity (QG) path integral. By exploiting this structure the models developed in CDTs differ from the analogous models developed in the Euclidean domain, models of (Euclidean) Dynamical Triangulations (DT), and the corresponding Lorentzian results are in many ways more "physical". In this paper we use this insight to formulate a Lorentzian signature model that is anal-ogous to the Quantum Regge Calculus (QRC) approach to Euclidean Quantum Gravity. We exploit another crucial fact about the structure of Lorentzian manifolds, namely that certain simplices are not constrained by the triangle inequalities present in Euclidean signa-ture. We show that this model is not related to QRC by a naive Wick rotation; this serves as another demonstration that the sum over Lorentzian geometries is not simply related to the sum over Euclidean geometries. By removing the triangle inequality constraints, there is more freedom to perform analytical calculations, and in addition numerical simulations are more computationally efficient. We first formulate the model in 1 + 1 dimensions, and derive scaling relations for the pure gravity path integral on the torus using two different measures. It appears relatively easy to generate "large" universes, both in spatial and temporal extent. In addition, loopto-loop amplitudes are discussed, and a transfer matrix is derived. We then also discuss the model in higher dimensions.

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

Science.gov (United States)

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

2018-07-13

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

Toward a microrealistic version of quantum mechanics. II

International Nuclear Information System (INIS)

Maxwell, N.

1976-01-01

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

Group contractions in quantum field theory

International Nuclear Information System (INIS)

Concini, C. De; Vitiello, G.

1979-01-01

General theorems are given for SU(n) and SO(n). A projective geometry argument is also presented with disclosure of the occurrence a group contraction mechanism as a geometric consequence of spontaneous breakdown of symmetry. It is also shown that a contraction of the conformal group gives account of the number of degrees of freedom of an n-pseudoparticle system in an Euclidean SU(2) gauge invariant Yang-Mills theory, in agreement with the result obtained by algebraic geometry methods. Low-energy theorems and ordered states symmetry patterns are observable manifestations of group contractions. These results seem to support the conjecture that the transition from quantum to classical physics involves a group contraction mechanism. (author)

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

Science.gov (United States)

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

2018-01-12

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

Nonlocality and localizability in quantum mechanics

International Nuclear Information System (INIS)

Matsuno, K.

1989-01-01

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

Introduction to quantum mechanics a time-dependent perspective

CERN Document Server

Tannor, David J

2007-01-01

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

Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces

Energy Technology Data Exchange (ETDEWEB)

Fu, Yu, E-mail: yufudufe@gmail.com [Dongbei University of Finance and Economics, School of Mathematics and Quantitative Economics (China)

2013-12-15

In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces.

Biharmonic Submanifolds with Parallel Mean Curvature Vector in Pseudo-Euclidean Spaces

International Nuclear Information System (INIS)

Fu, Yu

2013-01-01

In this paper, we investigate biharmonic submanifolds in pseudo-Euclidean spaces with arbitrary index and dimension. We give a complete classification of biharmonic spacelike submanifolds with parallel mean curvature vector in pseudo-Euclidean spaces. We also determine all biharmonic Lorentzian surfaces with parallel mean curvature vector field in pseudo-Euclidean spaces

Lectures in quantum mechanics a two-term course

CERN Document Server

Picasso, Luigi E

2016-01-01

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

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

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."

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

Energy Technology Data Exchange (ETDEWEB)

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

2010-11-01

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

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

International Nuclear Information System (INIS)

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

2010-01-01

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

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

International Nuclear Information System (INIS)

Basdevant, J.L.; Dalibard, J.

2006-01-01

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

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

International Nuclear Information System (INIS)

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

2006-01-01

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

Signature change events: a challenge for quantum gravity?

International Nuclear Information System (INIS)

White, Angela; Weinfurtner, Silke; Visser, Matt

2010-01-01

Within the framework of either Euclidean (functional integral) quantum gravity or canonical general relativity the signature of the manifold is a priori unconstrained. Furthermore, recent developments in the emergent spacetime programme have led to a physically feasible implementation of (analogue) signature change events. This suggests that it is time to revisit the sometimes controversial topic of signature change in general relativity. Specifically, we shall focus on the behaviour of a quantum field defined on a manifold containing regions of different signature. We emphasize that regardless of the underlying classical theory, there are severe problems associated with any quantum field theory residing on a signature-changing background. (Such as the production of what is naively an infinite number of particles, with an infinite energy density.) We show how the problem of quantum fields exposed to finite regions of Euclidean-signature (Riemannian) geometry has similarities with the quantum barrier penetration problem. Finally we raise the question as to whether signature change transitions could be fully understood and dynamically generated within (modified) classical general relativity, or whether they require the knowledge of a theory of quantum gravity.

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.

Cartoon computation: quantum-like computing without quantum mechanics

International Nuclear Information System (INIS)

Aerts, Diederik; Czachor, Marek

2007-01-01

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

Classical geometry Euclidean, transformational, inversive, and projective

CERN Document Server

Leonard, I E; Liu, A C F; Tokarsky, G W

2014-01-01

Features the classical themes of geometry with plentiful applications in mathematics, education, engineering, and science Accessible and reader-friendly, Classical Geometry: Euclidean, Transformational, Inversive, and Projective introduces readers to a valuable discipline that is crucial to understanding bothspatial relationships and logical reasoning. Focusing on the development of geometric intuitionwhile avoiding the axiomatic method, a problem solving approach is encouraged throughout. The book is strategically divided into three sections: Part One focuses on Euclidean geometry, which p

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

Extracontextuality and extravalence in quantum mechanics.

Science.gov (United States)

Auffèves, Alexia; Grangier, Philippe

2018-07-13

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

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.

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.)

Theoretical and quantum mechanics fundamentals for chemists

CERN Document Server

Ivanov, Stefan

2006-01-01

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

The non-Euclidean revolution

CERN Document Server

Trudeau, Richard J

1986-01-01

How unique and definitive is Euclidean geometry in describing the "real" space in which we live? Richard Trudeau confronts the fundamental question of truth and its representation through mathematical models in The Non-Euclidean Revolution. First, the author analyzes geometry in its historical and philosophical setting; second, he examines a revolution every bit as significant as the Copernican revolution in astronomy and the Darwinian revolution in biology; third, on the most speculative level, he questions the possibility of absolute knowledge of the world. Trudeau writes in a lively, entertaining, and highly accessible style. His book provides one of the most stimulating and personal presentations of a struggle with the nature of truth in mathematics and the physical world. A portion of the book won the Pólya Prize, a distinguished award from the Mathematical Association of America. "Trudeau meets the challenge of reaching a broad audience in clever ways...(The book) is a good addition to our literature o...

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.

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.

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.

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

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

Euclidean null controllability of perturbed infinite delay systems with ...

African Journals Online (AJOL)

Euclidean null controllability of perturbed infinite delay systems with limited control. ... Open Access DOWNLOAD FULL TEXT ... The results are established by placing conditions on the perturbation function which guarantee that, if the linear control base system is completely Euclidean controllable, then the perturbed system ...

Quaternion analyticity and conformally Kaehlerian structure in Euclidean gravity

International Nuclear Information System (INIS)

Guersey, F.; Chia-Hsiung Tze

1984-01-01

Starting from the fact that the d = 4 Euclidean flat spacetime is conformally related to the Kaehler manifold H 2 xS 2 , we show the Euclidean Schwarzschild metric to be conformally related to another Kaehler manifold M 2 xS 2 with M 2 being conformal to H 2 in two dimensions. Both metrics which are conformally Kaehlerian, are form-invariant under the infinite parameter Fueter group, the Euclidean counterpart of Milne's group of clock regraduation. The associated Einstein's equations translate into Fueter's quaternionic analyticity. The latter leads to an infinite number of local continuity equations. (orig.)

Quantum mechanics and dynamics in phase space

International Nuclear Information System (INIS)

Zlatev, I.S.

1979-01-01

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

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.

The cellular automaton interpretation of quantum mechanics

CERN Document Server

't Hooft, Gerard

2016-01-01

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

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

International Nuclear Information System (INIS)

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

2004-01-01

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

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

Science.gov (United States)

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

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

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.

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 ?

The Euclidean distance degree

NARCIS (Netherlands)

Draisma, J.; Horobet, E.; Ottaviani, G.; Sturmfels, B.; Thomas, R.R.; Zhi, L.; Watt, M.

2014-01-01

The nearest point map of a real algebraic variety with respect to Euclidean distance is an algebraic function. For instance, for varieties of low rank matrices, the Eckart-Young Theorem states that this map is given by the singular value decomposition. This article develops a theory of such nearest

New progress of fundamental aspects in quantum mechanics

International Nuclear Information System (INIS)

Sun Changpu

2001-01-01

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

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

Science.gov (United States)

Burnier, Yannis; Rothkopf, Alexander

2013-11-01

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T=2.33TC.

Quantum Backaction Evading Measurement of Collective Mechanical Modes.

Science.gov (United States)

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

2016-09-30

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

Testing quantum mechanics using third-order correlations

International Nuclear Information System (INIS)

Kinsler, P.

1996-01-01

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

Green functions and dimensional reduction of quantum fields on product manifolds

International Nuclear Information System (INIS)

Haba, Z

2008-01-01

We discuss Euclidean Green functions on product manifolds P=N x M. We show that if M is compact and N is not compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this approximation. We show that for large distances on N the remainder is small. If P=R D-1 x S β , where S β is a circle of radius β, then the result reduces to the well-known approximation of the D-dimensional finite temperature quantum field theory by (D - 1)-dimensional one in the high-temperature limit. Analytic continuation of Euclidean fields is discussed briefly

PERBANDINGAN EUCLIDEAN DISTANCE DENGAN CANBERRA DISTANCE PADA FACE RECOGNITION

Directory of Open Access Journals (Sweden)

Sendhy Rachmat Wurdianarto

2014-08-01

Full Text Available Perkembangan ilmu pada dunia komputer sangatlah pesat. Salah satu yang menandai hal ini adalah ilmu komputer telah merambah pada dunia biometrik. Arti biometrik sendiri adalah karakter-karakter manusia yang dapat digunakan untuk membedakan antara orang yang satu dengan yang lainnya. Salah satu pemanfaatan karakter / organ tubuh pada setiap manusia yang digunakan untuk identifikasi (pengenalan adalah dengan memanfaatkan wajah. Dari permasalahan diatas dalam pengenalan lebih tentang aplikasi Matlab pada Face Recognation menggunakan metode Euclidean Distance dan Canberra Distance. Model pengembangan aplikasi yang digunakan adalah model waterfall. Model waterfall beriisi rangkaian aktivitas proses yang disajikan dalam proses analisa kebutuhan, desain menggunakan UML (Unified Modeling Language, inputan objek gambar diproses menggunakan Euclidean Distance dan Canberra Distance. Kesimpulan yang dapat ditarik adalah aplikasi face Recognation menggunakan metode euclidean Distance dan Canverra Distance terdapat kelebihan dan kekurangan masing-masing. Untuk kedepannya aplikasi tersebut dapat dikembangkan dengan menggunakan objek berupa video ataupun objek lainnya.   Kata kunci : Euclidean Distance, Face Recognition, Biometrik, Canberra Distance

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

International Nuclear Information System (INIS)

Lee, Sang-Bong.

1993-09-01

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

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.

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

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.

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

International Nuclear Information System (INIS)

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

1990-01-01

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

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)

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

Science.gov (United States)

Hamada, Yojiro; Kanematsu, Yusuke; Tachikawa, Masanori

2016-10-11

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

Zeno dynamics in quantum statistical mechanics

International Nuclear Information System (INIS)

Schmidt, Andreas U

2003-01-01

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

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

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)

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

Science.gov (United States)

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

2018-01-01

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

A relationship between scalar Green functions on hyperbolic and Euclidean Rindler spaces

International Nuclear Information System (INIS)

Haba, Z

2007-01-01

We derive a formula connecting in any dimension the Green function on the (D + 1)-dimensional Euclidean Rindler space and the one for a minimally coupled scalar field with a mass m in the D-dimensional hyperbolic space. The relation takes a simple form in the momentum space where the Green functions are equal at the momenta (p 0 , p) for Rindler and (m,p-hat) for hyperbolic space with a simple additive relation between the squares of the mass and the momenta. The formula has applications to finite temperature Green functions, Green functions on the cone and on the (compactified) Milne spacetime. Analytic continuations and interacting quantum fields are briefly discussed

Entanglement, information, and the interpretation of quantum mechanics

International Nuclear Information System (INIS)

Jaeger, Gregg

2009-01-01

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

Bell trajectories for revealing quantum control mechanisms

International Nuclear Information System (INIS)

Dennis, Eric; Rabitz, Herschel

2003-01-01

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

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)

Quantum mechanics and the science of measurements

International Nuclear Information System (INIS)

Ramsey, N.F.

1992-01-01

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

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.

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)

Euclidean null controllability of nonlinear infinite delay systems with ...

African Journals Online (AJOL)

Sufficient conditions for the Euclidean null controllability of non-linear delay systems with time varying multiple delays in the control and implicit derivative are derived. If the uncontrolled system is uniformly asymptotically stable and if the control system is controllable, then the non-linear infinite delay system is Euclidean null ...

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

Science.gov (United States)

Plotnitsky, Arkady

2015-10-01

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

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.

Loop-quantum-gravity vertex amplitude.

Science.gov (United States)

Engle, Jonathan; Pereira, Roberto; Rovelli, Carlo

2007-10-19

Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one and it yields an SO(4)-covariant vertex amplitude for Euclidean loop gravity.

Quantum mechanical streamlines. I - Square potential barrier

Science.gov (United States)

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

1974-01-01

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

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

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.

Advanced quantum mechanics materials and photons

CERN Document Server

Dick, Rainer

2012-01-01

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

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.)

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...

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

African Journals Online (AJOL)

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

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

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

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...

Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model

Science.gov (United States)

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén

2018-05-01

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.

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)

Is string interaction the origin of quantum mechanics?

Energy Technology Data Exchange (ETDEWEB)

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

2014-12-12

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

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.

A probabilistic approach to quantum mechanics based on 'tomograms'

International Nuclear Information System (INIS)

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

2006-01-01

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

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)

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

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

CERN Document Server

Basdevant, Jean-Louis

2006-01-01

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

A mathematical companion to quantum mechanics

CERN Document Server

Sternberg, Shlomo

2019-01-01

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

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

Approach to measurement to quantum mechanics

International Nuclear Information System (INIS)

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

1977-10-01

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

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)

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

Science.gov (United States)

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

2012-11-07

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

Faithful conversion of propagating quantum information to mechanical motion

Science.gov (United States)

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

2017-12-01

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

Bohmian mechanics. The physics and mathematics of quantum theory

International Nuclear Information System (INIS)

Duerr, Detlef; Teufel, Stefan

2009-01-01

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

Bohmian mechanics. The physics and mathematics of quantum theory

Energy Technology Data Exchange (ETDEWEB)

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

2009-07-01

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

Quantum mechanics on the personal computer

International Nuclear Information System (INIS)

Brandt, S.; Dahmen, H.D.

1989-01-01

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

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.

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

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...

Individuation in Quantum Mechanics and Space-Time

Science.gov (United States)

Jaeger, Gregg

2010-10-01

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

Quantum Sensing of Mechanical Motion with a Single InAs Quantum Dot

Science.gov (United States)

2017-03-01

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

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

Science.gov (United States)

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

2010-04-01

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

John S. Bell on the foundations of quantum mechanics

CERN Document Server

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

2001-01-01

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

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 ...

Quantum cosmology and baby universes

International Nuclear Information System (INIS)

Grishchuk, L.P.

1990-01-01

The contributed papers presented to the workshop on ''Quantum Cosmology and Baby Universes'' have demonstrated the great interest in, and rapid development of, the field of quantum cosmology. In my view, there are at least three areas of active research at present. The first area can be defined as that of practical calculations. Here researchers are dealing with the basic quantum cosmological equation, which is the Wheeler-DeWitt equation. They try to classify all possible solutions to the Wheeler-DeWitt equation or seek a specific integration contour in order to select one particular wave function or generalize the simple minisuperspace models to more complicated cases, including various inhomogeneities, anisotropies, etc. The second area of research deals with the interpretational issues of quantum cosmology. There are still many questions about how to extract the observational consequences from a given cosmological wave function, the role of time in quantum cosmology, and how to reformulate the rules of quantum mechanics in such a way that they could be applicable to the single system which is our Universe. The third area of research is concerned with the so-called ''third quantization'' of gravity. In this approach a wave function satisfying the Wheeler-DeWitt equation becomes an operator acting on a Wave Function of the many-universes system. Within this approach one operates with Euclidean worm-holes joining different Lorentzian universes. (author)

Canonical Drude Weight for Non-integrable Quantum Spin Chains

Science.gov (United States)

Mastropietro, Vieri; Porta, Marcello

2018-03-01

The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous renormalization group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably, the proofs work for both integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous renormalization group methods, Ward identities, and complex analytic ideas.

Symmetry aspects in emergent quantum mechanics

Science.gov (United States)

Elze, Hans-Thomas

2009-06-01

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

Introductory quantum mechanics for semiconductor nanotechnology

International Nuclear Information System (INIS)

Kim, Dae Mann

2010-01-01

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

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

CERN Document Server

Pykacz, Jarosław

2015-01-01

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

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.

Towards spectral geometric methods for Euclidean quantum gravity

Science.gov (United States)

Panine, Mikhail; Kempf, Achim

2016-04-01

The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis, respectively. Of particular interest in this regard is the field of spectral geometry, which studies to which extent the shape of a Riemannian manifold is describable in terms of the spectra of differential operators defined on the manifold. Spectral geometry is hard because it is highly nonlinear, but linearized spectral geometry, i.e., the task to determine small shape changes from small spectral changes, is much more tractable and may be iterated to approximate the full problem. Here, we generalize this approach, allowing, in particular, nonequal finite numbers of shape and spectral degrees of freedom. This allows us to study how well the shape degrees of freedom are encoded in the eigenvalues. We apply this strategy numerically to a class of planar domains and find that the reconstruction of small shape changes from small spectral changes is possible if enough eigenvalues are used. While isospectral nonisometric shapes are known to exist, we find evidence that generically shaped isospectral nonisometric shapes, if existing, are exceedingly rare.

Quantum mechanics and hidden superconformal symmetry

Science.gov (United States)

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

2017-12-01

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

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…

On phase-space representations of quantum mechanics using

Indian Academy of Sciences (India)

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

The conceptual foundations of quantum mechanics

CERN Document Server

Eisenbud, Leonard

2007-01-01

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

Quantum mechanics as applied mathematical statistics

International Nuclear Information System (INIS)

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

2011-01-01

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

Three Dimensional Fast Exact Euclidean Distance (3D-FEED) Maps

NARCIS (Netherlands)

Latecki, L.J.; Schouten, Theo E.; Mount, D.M.; Kuppens, Harco C.; Wu, A.Y.; van den Broek, Egon

2006-01-01

In image and video analysis, distance maps are frequently used. They provide the (Euclidean) distance (ED) of background pixels to the nearest object pixel. Recently, the Fast Exact Euclidean Distance (FEED) transformation was launched. In this paper, we present the three dimensional (3D) version of

Euclidean null controllability of linear systems with delays in state ...

African Journals Online (AJOL)

Sufficient conditions are developed for the Euclidean controllability of linear systems with delay in state and in control. Namely, if the uncontrolled system is uniformly asymptotically stable and the control equation proper, then the control system is Euclidean null controllable. Journal of the Nigerian Association of ...

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

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.)

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.

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

Isometric immersions and embeddings of locally Euclidean metrics in R2

International Nuclear Information System (INIS)

Sabitov, I Kh

1999-01-01

This paper deals with the problem of isometric immersions and embeddings of two-dimensional locally Euclidean metrics in the Euclidean plane. We find explicit formulae for the immersions of metrics defined on a simply connected domain and a number of sufficient conditions for the existence of isometric embeddings. In the case when the domain is multiply connected we find necessary conditions for the existence of isometric immersions and classify the cases when the metric admits no isometric immersion in the Euclidean plane

Wavelet-Based Quantum Field Theory

Directory of Open Access Journals (Sweden)

Mikhail V. Altaisky

2007-11-01

Full Text Available The Euclidean quantum field theory for the fields $phi_{Delta x}(x$, which depend on both the position $x$ and the resolution $Delta x$, constructed in SIGMA 2 (2006, 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regularisation agrees with the existing calculations of radiative corrections to the electron magnetic moment. The transition from the newly constructed theory to a standard Euclidean field theory is achieved by integration over the scale arguments.

Random path formulation of nonrelativistic quantum mechanics

International Nuclear Information System (INIS)

Roncadelli, M.

1993-01-01

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

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)

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

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)

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)

Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and Thermodynamics

OpenAIRE

Beretta, Gian Paolo

2006-01-01

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

Quantum mechanics of charged particle beam optics

CERN Document Server

Khan, Sameen Ahmed

2018-01-01

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

The pure phases, the irreducible quantum fields, and dynamical symmetry breaking in Symanzik--Nelson positive quantum field theories

International Nuclear Information System (INIS)

Frohlich, J.

1976-01-01

We prove that a Symanzik--Nelson positive quantum field theory, i.e., a quantum field theory derived from a Euclidean field theory, has a unique decomposition into pure phases which preserves Symanzik--Nelson positivity and Poincare covariance. We derive useful sufficient conditions for the breakdown of an internal symmetry of such a theory in its pure phases, for the self-adjointness and nontrivially (in the sense of Borchers classes) of its quantum fields, and the existence of time-ordered and retarded products. All these general results are then applied to the P (phi) 2 and the phi 3 4 quantum field models

Quantum independent increment processes

CERN Document Server

Franz, Uwe

2005-01-01

This volume is the first of two volumes containing the revised and completed notes lectures given at the school "Quantum Independent Increment Processes: Structure and Applications to Physics". This school was held at the Alfried-Krupp-Wissenschaftskolleg in Greifswald during the period March 9 – 22, 2003, and supported by the Volkswagen Foundation. The school gave an introduction to current research on quantum independent increment processes aimed at graduate students and non-specialists working in classical and quantum probability, operator algebras, and mathematical physics. The present first volume contains the following lectures: "Lévy Processes in Euclidean Spaces and Groups" by David Applebaum, "Locally Compact Quantum Groups" by Johan Kustermans, "Quantum Stochastic Analysis" by J. Martin Lindsay, and "Dilations, Cocycles and Product Systems" by B.V. Rajarama Bhat.

Euclidean geometry and its subgeometries

CERN Document Server

Specht, Edward John; Calkins, Keith G; Rhoads, Donald H

2015-01-01

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...

Noncommutative products of Euclidean spaces

Science.gov (United States)

Dubois-Violette, Michel; Landi, Giovanni

2018-05-01

We present natural families of coordinate algebras on noncommutative products of Euclidean spaces R^{N_1} × _R R^{N_2} . These coordinate algebras are quadratic ones associated with an R -matrix which is involutive and satisfies the Yang-Baxter equations. As a consequence, they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces R4 × _R R4 . Among these, particularly well behaved ones have deformation parameter u \\in S^2 . Quotients include seven spheres S7_u as well as noncommutative quaternionic tori TH_u = S^3 × _u S^3 . There is invariance for an action of {{SU}}(2) × {{SU}}(2) on the torus TH_u in parallel with the action of U(1) × U(1) on a `complex' noncommutative torus T^2_θ which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.

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

International Nuclear Information System (INIS)

Ajanapon, P.

1985-01-01

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

Review of student difficulties in upper-level quantum mechanics

Directory of Open Access Journals (Sweden)

Chandralekha Singh

2015-09-01

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

Quantum mechanics in simple matrix form

CERN Document Server

Jordan, Thomas F

1986-01-01

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

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

International Nuclear Information System (INIS)

Engel, U.M.

2007-01-01

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

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.)

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

International Nuclear Information System (INIS)

Bell, John S.

2015-01-01

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

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...

Exponential complexity and ontological theories of quantum mechanics

International Nuclear Information System (INIS)

Montina, A.

2008-01-01

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

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

International Nuclear Information System (INIS)

Griffiths, David J.

2012-01-01

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

Experimental status of quaternionic quantum mechanics

International Nuclear Information System (INIS)

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

1995-01-01

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

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)

Introductory quantum mechanics for applied nanotechnology

CERN Document Server

Kim, Dae Mann

2015-01-01

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

A mathematical primer on quantum mechanics

CERN Document Server

Teta, Alessandro

2018-01-01

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

Horizon quantum mechanics of rotating black holes

Energy Technology Data Exchange (ETDEWEB)

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

2017-05-15

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

Molecules as quantum shapes and how they violate P and T

International Nuclear Information System (INIS)

Balachandran, A.P.; Witt, D.M.; Simoni, A.

1992-01-01

A geometric shape is a rigid shape in n-dimensional Euclidean space. These shapes commonly occur in the Born-Oppenheimer approximation in molecular physics, and collective models of nuclei. Abelian and non-Abelian generalizations of the of the vacuum angle of gauge theories are realized in the quantum theory of shapes. In this paper, such generalizations are presented in the language of modern quantum physics and it is shown that parity, P, and time reversal, T, are violated in certain of these quantum theories. However, the combined symmetry PT of parity composed with time reversal generally remains a good symmetry, just as in gauge theories. The exceptions are the quantum theories of staggered conformations which can violate only T. The mechanism responsible for the loss of these symmetries is a generalization of the vacuum angle mechanism for the same effect. An important results of the present analysis is the demonstration that geometric shapes, molecules in the Born-Oppenheimer approximation, and nuclei in the collective model description furnish concrete systems which upon quantization discriminate between left- and right-handed coordinates even though this distinction is entirely absent in their classical descriptions

Mayer expansions for Euclidean lattice field theory: Convergence properties and relation with perturbation theory

International Nuclear Information System (INIS)

Pordt, A.

1985-10-01

The author describes the Mayer expansion in Euclidean lattice field theory by comparing it with the statistical mechanics of polymer systems. In this connection he discusses the Borel summability and the analyticity of the activities on the lattice. Furthermore the relations between renormalization and the Mayer expansion are considered. (HSI)

Superconducting Qubits as Mechanical Quantum Engines.

Science.gov (United States)

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

2017-09-01

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

A linearization of quantum channels

Science.gov (United States)

Crowder, Tanner

2015-06-01

Because the quantum channels form a compact, convex set, we can express any quantum channel as a convex combination of extremal channels. We give a Euclidean representation for the channels whose inverses are also valid channels; these are a subset of the extreme points. They form a compact, connected Lie group, and we calculate its Lie algebra. Lastly, we calculate a maximal torus for the group and provide a constructive approach to decomposing any invertible channel into a product of elementary channels.

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.)

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

Quantum causality conceptual issues in the causal theory of quantum mechanics

CERN Document Server

Riggs, Peter J; French, Steven RD

2009-01-01

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

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

Science.gov (United States)

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

2014-06-13

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

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.