The Principles of Statistical Mechanics

Front Cover
Courier Corporation, Jan 1, 1979 - Science - 660 pages
Classic treatment of a subject essential to contemporary physics. Classical and quantum statistical mechanics, plus application to thermodynamic behavior.
 

Contents

PART ONE THE CLASSICAL STATISTICAL MECHANICS
1
THE ELEMENTS OF CLASSICAL MECHANICS
16
The Equations of Motion in the Lagrangian Form
25
Canonical Transformations
33
STATISTICAL ENSEMBLES IN THE CLASSICAL MECHANICS
43
Invariance of Density and of Extension to Canonical Transformations
52
The Fundamental Hypothesis of Equal a priori Probabilities in
59
Validity of Statistical Mechanics
65
Density Matrix Corresponding to a Pure State
333
Conditions for Statistical Equilibrium
339
The Fundamental Hypothesis of Equal a priori Probabilities
349
Validity of Statistical Quantum Mechanics
356
THE MAXWELLBOLTZMANN EINSTEINBOSE
362
The Probabilities for Different Conditions of the System
370
Distribution in Systems Containing Constituent Elements of More
374
EinsteinBose Systems
381

THE MAXWELLBOLTZMANN DISTRIBUTION
71
The Probabilities for Different Conditions of the System
78
MaxwellBoltzmann Distribution for Molecules of More Than a Single
82
Useful Forms of Expression for the Distribution Law
88
The General Principle of Equipartition
95
The Principles of Dynamical Reversibility and Reflectability
102
39 Molecular Constellations
108
The Closed Cycle of Corresponding Collisions
114
Application of Conservation Laws to Collisions
120
The Probability Coefficients for Collisions
127
BOLTZMANNS HTHEOREM
134
Discussion of the Htheorem
146
Htheorem and the Condition of Equilibrium
159
The Generalized Htheorem
165
The Necessity for Modifying Classical Ideas
180
B THE POSTULATES
189
The Operators Corresponding to Observable Quantities and their
195
General
206
Summary of Postulatory Basis
217
Waveparticle Duality De Broglie Waves for Free Particles
226
Correspondence between Classical and Quantum Mechanical Results
237
Characteristic States Eigenvalues and Eigenfunctions in General
246
Expansions in Terms of Eigenfunctions
254
Transformation Theory
261
The Method of Variation of Constants
273
Particle in Free Space
285
Particle in a Hookes Law Field of Force
291
Two Interacting Particles
299
75 Particles with Spin
306
Systems of Two or More Like Particles
312
STATISTICAL ENSEMBLES IN THE QUANTUM MECHANICS
325
94 FermiDirac Systems
388
THE CHANGE IN QUANTUM MECHANICAL SYSTEMS WITH TIME
395
Integration of Schroedinger Equation when an External Parameter
409
Observation and Specification of State in Studying the Change
416
TimeProportional Transitions
424
The Probabilities for Transition by Collision in FermiDirac
436
General Treatment of Changes in Ensembles with Time
450
Definition of H for a Representative Ensemble of Systems
459
106 Change of H with Time from the Exact Integration of the Schroe
466
Application of Htheorem to Interacting Systems
477
The Microcanonical Ensemble as Representing Equilibrium for
486
The Canonical Ensemble as Representing Equilibrium for a System
501
Equilibrium in MaxwellBoltzmann Systems
506
Equilibrium in General in PhysicalChemical Systems
519
The Energy Principle for Ensembles
528
StatisticalMechanical Analogues of Entropy Temperature
535
Effect on H of Adiabatic Changes in External Coordinates
541
Effect on H of Interaction in General
549
Carnot Cycle of Processes
556
FURTHER APPLICATIONS TO THERMODYNAMICS
565
Perfect Monatomic Gas
572
Crystals Composed of a Single Substance
583
Mixtures of Substances
595
Vapour Pressures and Chemical Equilibria
604
Equilibrium between Connected Systems
613
Fluctuations at Thermodynamic Equilibrium
629
Conclusion
649
Some Useful Formulae
655
NAME INDEX 661
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