Mathematical Foundations of Quantum Statistics

Name: Mathematical Foundations of Quantum Statistics
Brand: Dover Publications
Price: 18.99 EUR
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A. Y. Khinchin(Autor*in)

Dover Publications (Verlag)

Erschienen am 21. Februar 2013

459 Seiten

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978-0-486-16765-7 (ISBN)

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Inhalt

Intro
Title Page
Copyright Page
EDITOR'S PREFACE
Table of Contents
PREFACE
INTRODUCTION
Chapter I - PRELIMINARY CONCEPTS OF THE THEORY OF PROBABILITY
§1. Integral-valued random variables
§2. Limit theorems
§3. The method of characteristic functions
§4. The one-dimensional limit theorem
§5. The two-dimensional limit theorem
Chapter II - PRELIMINARY CONCEPTS OF QUANTUM MECHANICS
§1. Description of the state of a physical system in quantum mechanics
§2. Physical quantities and self-adjoint linear operators
§3. Possible values of physical quantities
§4. Evolution of the state of a system in time
§5. Stationary states. The law of conservation of energy
Chapter III - GENERAL PRINCIPLES OF QUANTUM STATISTICS
§1. Basic concepts of statistical methods in physics
§2. Microcanonical averages
§3. Complete, symmetric and antisymmetric statistics
§4. Construction of the fundamental linear basis
§5. Occupation numbers. Basic expressions of the structure functions
§6. On the suitability of microcanonical averages
Chapter IV - FOUNDATIONS OF THE STATISTICS OF PHOTONS
§1. Distinctive characteristics of the statistics of photons
§2. Occupation numbers and their mean values
§3. Reduction to a problem of the theory of probability
§4. Application of a limit theorem of the theory of probability
§5. The Planck formula
§6. On the suitability of microcanonical averages
Chapters V - FOUNDATIONS OF THE STATISTICS OF MATERIAL PARTICLES
§1. Review of fundamental concepts
§2. Mean values of the occupation numbers
§3. Reduction to a problem of the theory of probability
§4. Choice of values for the parameters a and ß
§5. Application of a limit theorem of the theory of probability
§6. Mean values of sum functions
§7. Correlation between occupation numbers
§8. Dispersion of sum functions and the suitability of microcanonical averages
§9. Determination of the numbers gk for structureless particles in the absence of external forces
Chapter VI - THERMODYNAMIC CONCLUSIONS
§1. The problems of statistical thermodynamics
§2. External parameters, external forces and their mean values
§3. The definition of entropy and the deduction of the second law of thermodynamics
Supplement I - THE STATISTICS OF HETEROGENEOUS SYSTEMS
Supplement II - THE DISTRIBUTION OF A COMPONENT AND ITS ENERGY
§1
§2
Supplement III - THE PRINCIPLE OF CANONICAL AVERAGING
Supplement IV - REDUCTION TO A ONE-DIMENSIONAL PROBLEM IN THE CASE OF COMPLETE STATISTICS
Supplement V - SOME GENERAL THEOREMS OF STATISTICAL PHYSICS [10]
§1
§2
§3
§4
§5
§6
§7
§8
§9
§10
Supplement VI - SYMMETRIC FUNCTIONS ON MULTI-DIMENSIONAL SURFACES [14]
§1. Introduction
§2. Preliminary formulas
§3. Distribution of the energy of a particle. Gibbs' theorem
§4. Derivation of the fundamental formula
§5. Distribution of the maximum and minimum energy of a particle
§6. The basic limit theorem
§7. Probability that the energy of a particle lies in a given interval
§8. A functional limit theorem
§9. Continuous symmetric functions
§10. Generalizations of Gibbs' theorem
REFERENCES
INDEX
A CATALOG OF SELECTED DOVER BOOKS IN SCIENCE AND MATHEMATICS

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