Synopses & Reviews
In this high-level mathematical treatment, a distinguished Russian mathematician introduces the mathematical underpinnings of quantum statistics in a manner accessible to both mathematicians and physicists. The book is aimed primarily at mathematicians, however, who will need only an elementary grasp of quantum physics to appreciate the author's well-organized and clearly written presentation. Beginning with preliminary concepts in the theory of probability, the text opens with a discussion and complete proofs of the limit theorems used in the main sections of the book. Proceeding to preliminary concepts and general principles of quantum mechanics, it examines the basis of the computational methods of quantum statistics and illustrates the means to achieve the statisticians' most important initial task: the determination of the mean values of occupation numbers. In addition, the foundations of the statistics of photons and material particles receive ample review.
Supplements to the concluding chapter on thermodynamics explore the distribution of a component and its energy, the principle of canonical averaging, symmetric functions on multidimensional surfaces, and other related topics.
Mathematicians with a basic understanding of quantum physics and physicists interested in the topic will benefit from this practical text. The treatment examines the basis of quantum statistical computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, and statistical thermodynamics. 1960 edition.
A coherent, well-organized look at the basis of quantum statistics computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.
Table of Contents
CHAPTER I. PRELIMINARY CONCEPTS OF THE THEORY OF PROBABILITY
CHAPTER II. PRELIMINARY CONCEPTS OF QUANTUM MECHANICS
CHAPTER III. GENERAL PRINCIPLES OF QUANTUM STATISTICS
CHAPTER IV. THE FOUNDATIONS OF THE STATISTICS OF PHOTONS
CHAPTER V. FOUNDATIONS OF THE STATISTICS OF MATERIAL PARTICLES
CHAPTER VI. THERMODYNAMIC CONCLUSIONS
Supplement I. THE STATISTICS OF HETEROGENEOUS SYSTEMS Supplement I I. THE DISTRIBUTION OF A COMPONENT AND ITS ENERGY Supplement III. THE PRINCIPLE OF CANONICAL AVERAGING Supplement IV. THE REDUCTION TO A ONE-DIMENSIONAL PROBLEM IN THE CASE OF COMPLETE STATISTICS Supplement V. SOME GENERAL THEOREMS OF STATISTICAL PHYSICS Supplement VI. SYMMETRIC FUNCTIONS ON MULTI-DIMENSIONAL SURFACES References Index