Quantum Mechanics In Phase Space: An Overview With Selected Papers
An Overview with Selected Papers
- 560 pages
- English
- PDF
- Available on iOS & Android
Quantum Mechanics In Phase Space: An Overview With Selected Papers
An Overview with Selected Papers
About this book
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.
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Table of contents
- CONTENTS
- Preface
- Overview of Phase-Space Quantization
- 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