The Principles of Statistical Mechanics
Classic treatment of a subject essential to contemporary physics. Classical and quantum statistical mechanics, plus application to thermodynamic behavior.
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Contents
PART ONE THE CLASSICAL STATISTICAL MECHANICS
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1 |
THE ELEMENTS OF CLASSICAL MECHANICS
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16 |
The Equations of Motion in the Lagrangian Form
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25 |
Canonical Transformations
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33 |
STATISTICAL ENSEMBLES IN THE CLASSICAL MECHANICS
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43 |
Invariance of Density and of Extension to Canonical Transformations
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52 |
The Fundamental Hypothesis of Equal a priori Probabilities in
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59 |
Validity of Statistical Mechanics
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65 |
Density Matrix Corresponding to a Pure State
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333 |
Conditions for Statistical Equilibrium
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339 |
The Fundamental Hypothesis of Equal a priori Probabilities
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349 |
Validity of Statistical Quantum Mechanics
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356 |
THE MAXWELLBOLTZMANN EINSTEINBOSE
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362 |
The Probabilities for Different Conditions of the System
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370 |
Distribution in Systems Containing Constituent Elements of More
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374 |
EinsteinBose Systems
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381 |
THE MAXWELLBOLTZMANN DISTRIBUTION
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71 |
The Probabilities for Different Conditions of the System
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78 |
MaxwellBoltzmann Distribution for Molecules of More Than a Single
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82 |
Useful Forms of Expression for the Distribution Law
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88 |
The General Principle of Equipartition
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95 |
The Principles of Dynamical Reversibility and Reflectability
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102 |
39 Molecular Constellations
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108 |
The Closed Cycle of Corresponding Collisions
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114 |
Application of Conservation Laws to Collisions
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120 |
The Probability Coefficients for Collisions
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127 |
BOLTZMANNS HTHEOREM
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134 |
Discussion of the Htheorem
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146 |
Htheorem and the Condition of Equilibrium
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159 |
The Generalized Htheorem
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165 |
The Necessity for Modifying Classical Ideas
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180 |
B THE POSTULATES
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189 |
The Operators Corresponding to Observable Quantities and their
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195 |
General
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206 |
Summary of Postulatory Basis
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217 |
Waveparticle Duality De Broglie Waves for Free Particles
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226 |
Correspondence between Classical and Quantum Mechanical Results
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237 |
Characteristic States Eigenvalues and Eigenfunctions in General
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246 |
Expansions in Terms of Eigenfunctions
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254 |
Transformation Theory
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261 |
The Method of Variation of Constants
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273 |
Particle in Free Space
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285 |
Particle in a Hookes Law Field of Force
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291 |
Two Interacting Particles
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299 |
75 Particles with Spin
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306 |
Systems of Two or More Like Particles
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312 |
STATISTICAL ENSEMBLES IN THE QUANTUM MECHANICS
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325 |
94 FermiDirac Systems
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388 |
THE CHANGE IN QUANTUM MECHANICAL SYSTEMS WITH TIME
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395 |
Integration of Schroedinger Equation when an External Parameter
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409 |
Observation and Specification of State in Studying the Change
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416 |
TimeProportional Transitions
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424 |
The Probabilities for Transition by Collision in FermiDirac
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436 |
General Treatment of Changes in Ensembles with Time
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450 |
Definition of H for a Representative Ensemble of Systems
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459 |
106 Change of H with Time from the Exact Integration of the Schroe
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466 |
Application of Htheorem to Interacting Systems
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477 |
The Microcanonical Ensemble as Representing Equilibrium for
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486 |
The Canonical Ensemble as Representing Equilibrium for a System
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501 |
Equilibrium in MaxwellBoltzmann Systems
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506 |
Equilibrium in General in PhysicalChemical Systems
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519 |
The Energy Principle for Ensembles
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528 |
StatisticalMechanical Analogues of Entropy Temperature
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535 |
Effect on H of Adiabatic Changes in External Coordinates
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541 |
Effect on H of Interaction in General
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549 |
Carnot Cycle of Processes
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556 |
FURTHER APPLICATIONS TO THERMODYNAMICS
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565 |
Perfect Monatomic Gas
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572 |
Crystals Composed of a Single Substance
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583 |
Mixtures of Substances
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595 |
Vapour Pressures and Chemical Equilibria
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604 |
Equilibrium between Connected Systems
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613 |
Fluctuations at Thermodynamic Equilibrium
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629 |
Conclusion
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649 |
Some Useful Formulae
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655 |
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Common terms and phrases
accordance actual angular momentum apply appropriate approximate behaviour canonical distribution canonical ensemble classical mechanics collision components condition connexion consider constant constellation coordinates and momenta corresponding denote density matrix dependence eigenfunctions eigensolutions eigenstates eigenvalues Einstein-Bose electron elements entropy equal a priori equilibrium evident expression Fermi-Dirac fluctuations function Gibbs give given grand canonical ensemble H-theorem Hamiltonian Hence Hermitian initial integration isolated system kind Maxwell-Boltzmann Maxwell-Boltzmann distribution mean energy mean value mechanical system methods microcanonical microcanonical ensemble number of particles numbers of molecules observation obtain operator P₁ parameter phase space possible precise principle probability amplitude probability of finding properties quantity H quantum mechanical rate of change regarded relation representative ensemble result Schroedinger equation solution specified statistical mechanics summation system of interest system proper temperature thermodynamic equilibrium thermodynamic system tion total number transformation treated treatment variables velocities write zero Σπί