Phase Space Picture Of Quantum Mechanics
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Phase Space Picture Of Quantum Mechanics
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Author : Y. S. Kim
language : en
Publisher: World Scientific
Release Date : 1991
Phase Space Picture Of Quantum Mechanics written by Y. S. Kim and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Science categories.
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 Schrdinger 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.
Quantum Mechanics In Phase Space
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Author : Cosmas Zachos
language : en
Publisher: World Scientific
Release Date : 2005
Quantum Mechanics In Phase Space written by Cosmas Zachos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
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.
Quantum Mechanics On Phase Space
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Author : Surya Ganguli
language : en
Publisher:
Release Date : 1998
Quantum Mechanics On Phase Space written by Surya Ganguli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Quantum Mechanics On Phase Space
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Author : Franklin E. Schroeck Jr.
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Quantum Mechanics On Phase Space written by Franklin E. Schroeck Jr. and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
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].
The Physics Of Phase Space
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Author : Young S. Kim
language : en
Publisher: Springer
Release Date : 2005-09-13
The Physics Of Phase Space written by Young S. Kim and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-13 with Science categories.
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.
The Picture Book Of Quantum Mechanics
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Author : Siegmund Brandt
language : en
Publisher: Springer
Release Date : 2011-06-28
The Picture Book Of Quantum Mechanics written by Siegmund Brandt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Science categories.
This book aims to provide an intuitive understanding of wave mechanics by using computer generated illustrations to present the time evolution and parameter dependence of wave functions for one and three-dimensional systems. The situations discussed range from the simple particle in a box through resonant scattering in one dimension to the hydrogen atom and Regge classification of resonant scattering. The text helps students to establish the relation between quantum mechanics and classical physics.
The Picture Book Of Quantum Mechanics
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Author : Siegmund Brandt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-18
The Picture Book Of Quantum Mechanics written by Siegmund Brandt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-18 with Science categories.
The aim of this book is to explain the basic concepts and phenomena of quantum mechanics by means of visualisation. Computer-generated illustrations in color are used extensively throughout the text, helping to establish the relation between quantum mechanics—wave functions, interference, atomic structure, and so forth—and classical physics—point mechanics, statistical mechanics, and wave optics. Even more important, by studying the pictures in parallel with the text, readers develop an intuition for such notoriously abstract phenomena as: the tunnel effect excitation and decay of metastable states wave-packet motion within a well systems of distinguishable and indistinguishable particles free wave packets and scattering in 3 dimensions angular-momentum decomposition stationary bound states in various 3-dimensional potentials hybrid states Kepler motion of wave packets in the Coulomb field spin and magnetic resonance Illustrations from experiments in a variety of fields, including chemistry, and molecular, atomic, nuclear, and particle physics, underline the basic as well as the practical importance of quantum mechanics. In the present, fourth edition all computer graphics are presented in full colour. It also contains additional physics topics such as hybridisation.
Linear Ray And Wave Optics In Phase Space
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Author : Amalia Torre
language : en
Publisher: Elsevier
Release Date : 2005-11-11
Linear Ray And Wave Optics In Phase Space written by Amalia Torre and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-11 with Science categories.
Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means. At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner function based technique as the mathematical machinery to accommodate between the two opposite extremes of light representation: the localized ray of geometrical optics and the unlocalized wave function of wave optics. At a parallel level, the analogies with other branches of both classical and quantum physics, like classical and quantum mechanics, quantum optics, signal theory as well as magnetic optics, are evidenced by pertinent comments and/or rigorous mathematics. So, the Lie algebra and group methods are introduced and explained through the elementary optical systems within both the ray and wave optics contexts, the former being related to the symplectic group and the latter to the metaplectic group. In a like manner, the Wigner function is introduced by following the original issue to individualize a phase space representation of quantum mechanics, which is mirrored by the issue to individualize a local frequency spectrum within the signal theory context. The basic analogy with the optics of charged particles inherently underlying the ray-optics picture in phase space is also evidenced within the wave-optics picture in the Wigner phase space. · amalgamation of a great deal of contributions having witnessed the phase space picture of optics over the past 30 years · introduces abstract concepts through concrete systems · hosts of figures and logical diagrams to favour intuition and to introduce mathematics · emphasis on the interrelations with quantum optics, signal theory and magnetic optics · feeds a feeling for genuine issues in higher mathematics and theoretical physics
Quantum Mechanics
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Author : Mark Julian Everitt
language : en
Publisher: John Wiley & Sons
Release Date : 2023-09-08
Quantum Mechanics written by Mark Julian Everitt and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-08 with Science categories.
QUANTUM MECHANICS From classical analytical mechanics to quantum mechanics, simulation, foundations & engineering Quantum mechanics is a fundamental and conceptually challenging area of physics. It is usually assumed that students are unfamiliar with Lagrangian and Hamiltonian formulations of classical mechanics and the role played by probability. As a result, quantum physics is typically introduced using heuristic arguments, obscuring synergies with classical mechanics. This book takes an alternative approach by leveraging classical analytical mechanics to facilitate a natural transition to quantum physics. By doing so, a solid foundation for understanding quantum phenomena is provided. Key features of this textbook include: Mathematics and Classical Analytical Mechanics: The necessary mathematical background and classical analytical mechanics are introduced gradually, allowing readers to focus on one conceptual challenge at a time. Deductive Approach: Quantum mechanics is presented on the firm foundation of classical analytical mechanics, ensuring a logical progression of concepts. Pedagogical Features: This book includes helpful notes, worked examples, problems, computational challenges, and problem-solving approaches to enhance understanding. Comprehensive Coverage: Including advanced topics such as open quantum systems, phase-space methods, and computational methods for quantum physics including good programming practice and code design. Much of the code needed to reproduce figures throughout this book is included. Consideration of Foundations: The measurement problem and correspondence principle are addressed, including an open and critical discussion of their interpretation and consequences. Introduction to Quantum Systems Engineering: This is the first book to introduce Quantum Systems Engineering approaches for applied quantum technologies development. This textbook is suitable for undergraduate students in physics and graduate students in mathematics, chemistry, engineering, and materials science.
Quantum Interferometry In Phase Space
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Author : Martin Suda
language : en
Publisher: Springer Science & Business Media
Release Date : 2006
Quantum Interferometry In Phase Space written by Martin Suda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
"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.