Quantum Mechanics In Phase Space

Author : Cosmas Zachos,David Fairlie,Thomas Curtright
Publisher : World Scientific
Page : 560 pages
File Size : 50,6 Mb
Release : 2005
Category : Science
ISBN : 9789812383846

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Quantum Mechanics in Phase Space by Cosmas Zachos,David Fairlie,Thomas Curtright Pdf

Wigner's quasi-probability distribution function in phase space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence, quantum computing, and quantum chaos. It is also important in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative, formulation of quantum mechanics, independent of the conventional Hilbert space, or path integral formulations.In this logically complete and self-standing formulation, one need not choose sides ? coordinate or momentum space. It works in full phase space, accommodating the uncertainty principle, and it offers unique insights into the classical limit of quantum theory. This invaluable book is a collection of the seminal papers on the formulation, with an introductory overview which provides a trail map for those papers; an extensive bibliography; and simple illustrations, suitable for applications to a broad range of physics problems. It can provide supplementary material for a beginning graduate course in quantum mechanics.

Author : Thomas L Curtright,David B Fairlie,Cosmas K Zachos
Publisher : World Scientific Publishing Company
Page : 172 pages
File Size : 46,6 Mb
Release : 2013-11-11
Category : Science
ISBN : 9789814520461

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A Concise Treatise on Quantum Mechanics in Phase Space by Thomas L Curtright,David B Fairlie,Cosmas K Zachos Pdf

This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions — density matrices in a special Weyl representation — and star products are the cornerstones of the formalism. The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. In this logically complete and self-standing formulation, one need not choose sides between coordinate or momentum space variables. It works in full phase space, accommodating the uncertainty principle; and it offers unique insights into the classical limit of quantum theory. The observables in this formulation are c-number functions in phase space instead of operators, with the same interpretation as their classical counterparts, only composed together in novel algebraic ways using star products. This treatise provides an introductory overview and supplementary material suitable for an advanced undergraduate or a beginning graduate course in quantum mechanics.

Author : Y S Kim,M E Noz
Publisher : World Scientific
Page : 352 pages
File Size : 40,5 Mb
Release : 1991-03-06
Category : Science
ISBN : 9789814506670

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Phase Space Picture of Quantum Mechanics by Y S Kim,M E Noz Pdf

This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schrödinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects. Contents:Phase Space in Classical MechanicsForms of Quantum MechanicsWigner Phase- Space Distribution FunctionsLinear Canonical Transformations in Quantum MechanicsCoherent and Squeezed StatesPhase-Space Picture of Coherent and Squeezed StatesLorentz TransformationsCovariant Harmonic OscillatorsLorentz-Squeezed HadronsSpace-Time Geometry of Extended Particles Readership: Physicists, applied physicists and mathematical physicists. keywords:Lorentz Transformations;Wigner's Little Groups;Quantum Optics;Relativistic Quantum Mechanics;Phase Space;Wigner Function;Squeezed States;Feynman's Parton Picture;Covariant Harmonic Oscillators;Space-Time Geometry;Hadrons;Group Theory “… if Casimir invariants and Lorentz groups excite you, you'll be at home in Kim and Noz's lecture notes…” Contemporary Physics

Author : Franklin E. Schroeck Jr
Publisher : Unknown
Page : 692 pages
File Size : 55,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401728313

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Quantum Mechanics on Phase Space by Franklin E. Schroeck Jr Pdf

Author : Wolfgang P. Schleich
Publisher : John Wiley & Sons
Page : 716 pages
File Size : 47,7 Mb
Release : 2015-12-11
Category : Science
ISBN : 9783527802555

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Quantum Optics in Phase Space by Wolfgang P. Schleich Pdf

Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

Author : Y. S. Kim,Marilyn E. Noz
Publisher : World Scientific
Page : 356 pages
File Size : 40,7 Mb
Release : 1991
Category : Science
ISBN : 9810203616

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Phase Space Picture of Quantum Mechanics by Y. S. Kim,Marilyn E. Noz Pdf

This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed, in addition to the conventional Schr”dinger or Heisenberg picture. It is shown that the uncertainty relation can be represented more accurately in this picture. In addition, the phase space picture is shown to be the natural representation of quantum mechanics for modern optics and relativistic quantum mechanics of extended objects.

Author : Franklin Schroeck
Publisher : Springer
Page : 696 pages
File Size : 54,7 Mb
Release : 1996
Category : Mathematics
ISBN : UOM:39015037456129

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Quantum Mechanics on Phase Space by Franklin Schroeck Pdf

Offers a new mathematical formulation of quantum theory, clarifies a number of discrepancies within the prior formulation, describes new applications to experiments in physics, and extends the realm of application beyond physics to such fields as signal processing and neuroscience. The approach is based on new extensions of the theory of group representations, which are developed and illustrated in the text, and connects quantum theory with quantum logic, philosophy, and the history of science. Assumes a knowledge of basic topology and analysis, some modern abstract algebra, and at least rudimentary quantum mechanics. Annotation copyright by Book News, Inc., Portland, OR

Author : Philip Watson
Publisher : Unknown
Page : 128 pages
File Size : 54,5 Mb
Release : 1991
Category : Phase space (Statistical physics)
ISBN : OCLC:1108942100

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Quantum Mechanics in Phase Space by Philip Watson Pdf

Author : Franklin E. Schroeck Jr.
Publisher : Springer Science & Business Media
Page : 672 pages
File Size : 40,5 Mb
Release : 2013-06-29
Category : Science
ISBN : 9789401728300

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Quantum Mechanics on Phase Space by Franklin E. Schroeck Jr. Pdf

In this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967].

Author : G. B. Folland
Publisher : Princeton University Press
Page : 292 pages
File Size : 55,5 Mb
Release : 1989-03-21
Category : Mathematics
ISBN : 0691085285

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Harmonic Analysis in Phase Space by G. B. Folland Pdf

This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

Author : David Marcus Appleby
Publisher : Unknown
Page : 128 pages
File Size : 49,7 Mb
Release : 1997
Category : Electronic
ISBN : OCLC:59428025

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Quantum Mechanics on Phase Space by David Marcus Appleby Pdf

Author : Young S. Kim,Woodford W. Zachary
Publisher : Springer
Page : 452 pages
File Size : 40,7 Mb
Release : 2006-01-20
Category : Science
ISBN : 9783540479017

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The Physics of Phase Space by Young S. Kim,Woodford W. Zachary Pdf

The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study of the Wigner distribution. This volume gives the first complete survey of the progress made by both mathematicians and physicists. It will serve as an excellent reference for further research.

Author : Kurt Bernardo Wolf
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 41,5 Mb
Release : 2004-07-21
Category : Science
ISBN : 3540220399

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Geometric Optics on Phase Space by Kurt Bernardo Wolf Pdf

Symplectic geometry, well known as the basic structure of Hamiltonian mechanics, is also the foundation of optics. In fact, optical systems (geometric or wave) have an even richer symmetry structure than mechanical ones (classical or quantum). The symmetries underlying the geometric model of light are based on the symplectic group. Geometric Optics on Phase Space develops both geometric optics and group theory from first principles in their Hamiltonian formulation on phase space. This treatise provides the mathematical background and also collects a host of useful methods of practical importance, particularly the fractional Fourier transform currently used for image processing. The reader will appreciate the beautiful similarities between Hamilton's mechanics and this approach to optics. The appendices link the geometry thus introduced to wave optics through Lie methods. The book addresses researchers and graduate students.

Author : De Gosson Maurice A
Publisher : World Scientific
Page : 424 pages
File Size : 46,9 Mb
Release : 2016-11-10
Category : Science
ISBN : 9789813200982

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Principles Of Newtonian And Quantum Mechanics, The: The Need For Planck's Constant, H (Second Edition) by De Gosson Maurice A Pdf

The second edition of this book deals, as the first, with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. We have revised and augmented the topics studied in the first edition in the light of new results, and added several new sections. The Bohmian interpretation of quantum mechanics is discussed in detail. Phase space quantization is achieved using the "principle of the symplectic camel", which is a deep topological property of Hamiltonian flows. We introduce the notion of "quantum blob", which can be viewed as the fundamental phase space unit. The mathematical tools developed in this book are the theory of the symplectic and metaplectic group, the Maslov index in a rigorous form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introduced, in connection with the Bohmian theory of motion. The short-time behavior of the propagator is studied and applied to the quantum Zeno effect.

Author : Martin Suda
Publisher : Springer Science & Business Media
Page : 204 pages
File Size : 55,7 Mb
Release : 2006
Category : Science
ISBN : 3540260706

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Quantum Interferometry in Phase Space by Martin Suda Pdf

"Quantum Interferometry in Phase Space" is primarily concerned with quantum-mechanical distribution functions and their applications in quantum optics and neutron interferometry. In the first part of the book, the author describes the phase-space representation of quantum optical phenomena such as coherent and squeezed states. Applications to interferometry, e.g. in beam splitters and fiber networks, are also presented. In the second part of the book, the theoretical formalism is applied to neutron interferometry, including the dynamical theory of diffraction, coherence properties of superposed beams, and dephasing effects.