The enigma of probability and physics

by Lazar Mayants

[目次]

  • I. Fundamentals of Probabilistics.- 1 / Principal Concepts.- 1.1. Concrete Objects.- 1.2. Abstract Objects.- 1.3. More about Concrete and Abstract Objects.- 1.4. Measure of a Set of Concrete Objects.- 1.5. Experimental Determination of the Measures of Sets of Concrete Objects.- 1.6. The Statistical Method.- 1.7. Probability. Preliminary Consideration.- 1.8. Mutually Adequate Sets.- 1.9. Probability. General Definition.- Problems.- Suggested References.- 2 / Main Theorems.- 2.1. Sum and Product of Events.- 2.2. Addition Theorem.- 2.3. Multiplication Theorem.- 2.4. Sequence of Random Tests.- 2.5. Law of Large Numbers.- 2.6. Limiting Cases of Binomial Law.- Problems.- Suggested References.- 3 / Random Variables.- 3.1. Definition.- 3.2. Probability Distribution.- 3.3. Joint Probability Distribution for Functions of Random Variables.- 3.4. Mathematical Expectation. Moments.- 3.5. Characteristic Function.- Problems.- Suggested References.- 4 / Some Aspects of Statistics.- 4.1. Preliminary Considerations.- 4.2. Statistical Experiment.- 4.3. Numerical Statistical Experiment.- 4.4. Concluding Remarks.- Suggested References.- 5 / States of Abstract Objects.- 5.1. Introductory Remarks.- 5.2. Description of States.- 5.3. Necessary Mathematics.- 5.4. Two Specific Modes of Description of a State.- 5.5. Additional Mathematics.- Problems.- Suggested References.- 6 / Hamiltonian Random Variables.- 6.1. Lagrangian Equations and Hamiltonian Equations.- 6.2. Hamiltonian Random Variables.- 6.3. Canonically Conjugate Operators.- 6.4. Quantum Approach.- 6.5. Standard Deviations of Canonically Conjugate Random Variables.- Problems.- Suggested References.- 7 / Random Fields.- 7.1. Definition.- 7.2. Two Types of Related Finite-Dimensional Random Variables.- 7.1. Lagrangian and Hamiltonian Partial Equations.- 7.2. Hamiltonian Random Fields.- Suggested References.- II. Fundamentals of Probabilistic Physics.- 8 / General Considerations.- 8.1. Preliminaries.- 8.2. Classification of Physical Systems.- 8.3. Two Possible Types of Problems.- 8.4. Conservation Laws.- Suggested References.- 9 / Equilibrium Classical Statistical Mechanics.- 9.1. Microcanonical Distribution.- 9.2. Canonical Distribution.- 9.3. A Separate Atom in a Thermostat.- 9.4. Thermodynamic Functions.- 9.5. The Ideal (Perfect) Gas.- 9.6. Important Notes.- Suggested Reference.- 10 / Quantum Mechanics.- 10.1. Principal Propositions.- 10.2. Operators for Physical Quantities.- 10.2.1. Coordinates and Momenta.- 10.2.2. Time and Energy.- 10.2.3. Hamiltonian.- 10.2.4. Angular Momentum.- 10.2.5. Derivatives.- 10.2.6. Quantities Having a Finite Number of Values.- 10.3. Schrodinger Equation.- 10.4. A Free Particle.- 10.5. A Particle in a One-Dimensional Potential Box.- 10.6. One-Dimensional Harmonic Oscillator.- 10.7. A Particle in a Central Field.- 10.8. Equilibrium Quantum Statistical Mechanics.- Problems.- Suggested References.- 11 / Kinetics of Physical Transformations.- 11.1. Processes in Concrete Physical Systems.- 11.2. Probabilistic Treatment of Transformations.- 11.3. Basic Principles of the Transitional Configuration Theory.- 11.4. Leaving a Potential Well Through a Potential Barrier.- 11.5. Nonexponential Decay Law.- 11.6. Intramolecular Rearrangements.- 11.7. A Criterion of the Possibility of an Intramolecular Rearrangement.- Problems.- Suggested References.- 12 / Electromagnetic Field and Photons.- 12.1. Preliminaries.- 12.2. The Four-Dimensional Space Treatment.- 12.3. Physical Consideration.- 12.4. The Emon.- 12.5. Relativistic Aberration and Doppler Effect.- Problems.- Suggested References.- III. Methodological Problems.- 13 / Problems Related to Probability.- 13.1. Basic Phenomenon of Probabilistics.- 13.2. Mises' Definition of Probability.- 13.3. Kolmogorov's Probability Theory.- 13.4. Bertrand Paradox 285 Bibliography.- 14 / Problems Related to Physics.- 14.1. Gibbs' Paradox and Indistinguishability of Particles.- 14.2. Classical Limit of Quantum Mechanics.- 14.3 Energy and Time.- 14.4. One-Particle Relativistic Equations.- 14.5. Possible States of a Conservative System.- 14.6. Conventional Decay Theories.- 14.7.Time-Energy Uncertainty Relation.- 14.8. Measurement and Related Problems.- 14.1. Wave-Corpuscle Duality and Reality of Motion.- 14.2. Reality of Motion and Potential Energy.- 14.3. Einstein-Podolsky-Rosen's Paradox.- 14.4. Bell's Theorem.- 14.5. Second Quantization.- Appendix 1. Proof of Equations (6.16") and (6.16").- Appendix 2. Derivation of Equations of Section 6.3.- Appendix 3. A General Rotation-Vibration Hamiltonian.- Answers to Problems.

「Nielsen BookData」より

この本の情報

書名 The enigma of probability and physics
著作者等 Mayants, Lazar
シリーズ名 Fundamental theories of physics
出版元 D. Reidel Pub. Co;Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers
刊行年月 c1984
ページ数 xx, 373 p.
大きさ 25 cm
ISBN 9027716749
NCID BA06552182
※クリックでCiNii Booksを表示
言語 英語
出版国 オランダ
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想