Quantum Mechanics In Phase Space : An Overview With Selected Papers.
Başlık:
Quantum Mechanics In Phase Space : An Overview With Selected Papers.
Yazar:
Zachos , Cosmas K.
ISBN:
9789812703507
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 online resource (560 pages)
İçerik:
CONTENTS -- Preface -- Overview of Phase-Space Quantization -- 1 Introduction -- 2 The Wigner Function -- 3 Solving for the Wigner Function -- 4 The Uncertainty Principle -- 5 Ehrenfest's Theorem -- 6 Illustration: The Harmonic Oscillator -- 7 Time Evolution -- 8 Nondiagonal Wigner Functions -- 9 Stationary Perturbation Theory -- 10 Propagators -- 11 Canonical Transformations -- 12 The Weyl Correspondence -- 13 Alternate Rules of Association -- 14 The Groenewold-van Hove Theorem and the Uniqueness of MBs and *-Products -- 15 Omitted Miscellany -- 16 Selected Papers: Brief Historical Outline -- References -- List of Selected Papers -- Index -- Quantenmechanik und Gruppentheorie -- Die Eiudeutigkeit der Schrodingerschen Operatoren -- On the Quantum Correction For Thermodynamic Equilibrium -- ON THE PRINCIPLES OF ELEMENTARY QUANTUM MECHANICS -- QUANTUM MECHANICS AS A STATISTICAL THEORY -- THE EXACT TRANSITION PROBABILITIES O F QUANTUM- MECHANICAL OSCILLATORS CALCULATED BY THE PHASE-SPACE METHOD -- The Formulation of Quantum Mechanics in terms of Ensemble in Phase Space'' -- Formulation of Quantum Mechanics Based on the Quasi-Probability Distribution Induced on Phase Space -- The formulation of quantum mechanics in terms of phase space functions -- A NON-NEGATIVE WIGNER-TYPE DISTRIBUTION -- Wigner function as the expectation value of a parity operator -- Deformation Theory and Quantization -- Deformation Theory and Quantization II. Physical Applications -- Wigner distribution functions and the representation of canonical transformations in quantum mechanics -- Wigner's phase space function and atomic structure -- DISTRIBUTION FUNCTIONS IN PHYSICS: FUNDAMENTALS -- Canonical transformation in quantum mechanics -- Negative probability -- EXISTENCE OF STAR-PRODUCTS AND OF FORMAL DEFORb4ATIONS OF THE POISSON LIE ALGEBRA OF ARBITRARY SYMPLECTIC MANIFOLDS.
A SIMPLE GEOMETRICAL CONSTRUCTION OF DEFORMATION QUANTIZATION -- Features of time-independent Wigner functions -- NEGATIVE PROBABILITY AND UNCERTAINTY RELATIONS -- Generating all Wigner functions -- Modified spectral method in phase space: Calculation of the Wigner function. I. Fundamentals -- Modified spectral method in phase space: Calculation of the Wigner function. II. Generalizations.
Özet:
Wignerâs 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 â 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.
Notlar:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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