Statistical Mechanics,9781891389153

Statistical Mechanics

by
ISBN13: 9781891389153
ISBN10: 1891389157
Format: Hardcover
Pub. Date: 2000-02-01
Publisher(s): Univ Science Books
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Table of Contents

Preface xi
Introduction and Review
1(34)
Introduction
1(2)
Classical Mechanics
3(5)
Quantum mechanics
8(5)
Thermodynamics
13(7)
Mathematics
20(15)
The Canonical Ensemble
35(16)
Ensemble Averages
35(2)
Method of the Most Probable Distribution
37(3)
The Evaluation of the Undetermined Multipliers, α and β
40(4)
Thermodynamic Connection
44(7)
Other Ensemble and Fluctuations
51(17)
Grand canonical Ensemble
51(4)
Other Ensembles
55(2)
Fluctuations
57(11)
Boltzmann Statistics, Fermi-Dirac Statistics, and Bose-Einstein Statistics
68(13)
The Special Case of Boltzmann Statistics
68(5)
Fermi-Dirac and Bose-Einstein Statistics
73(8)
Ideal Monatomic Gas
81(10)
The Translational Partition Function
81(2)
The Electronic and Nuclear Partition Functions
83(2)
Thermodynamic Functions
85(2)
A Digression on Atomic Term Symbols
87(4)
Ideal Diatomic Gas
91(22)
The Rigid Rotor-Harmonic Oscillator Approximation
91(5)
The Vibrational Partition Function
96(2)
The Rotational Partition Function of a Heteronuclear Diatomic Molecule
98(3)
The Symmetry Requirement of the Total Wave Function of a Homonuclear Diatomic Molecule
101(3)
The Rotational Partition Function of a Homonuclear Diatomic Molecule
104(4)
Thermodynamic Functions
108(5)
Classical Statistical Mechanics
113(16)
The Classical Partition Function
113(4)
Phase Space and the Liouville Equation
117(4)
Equipartition of Energy
121(8)
Ideal Polyatomic Gas
129(13)
The Vibrational Partition Function
130(3)
The Rotational Partition Function
133(3)
Thermodynamic Functions
136(2)
Hindered Rotation
138(4)
Chemical Equilibrium
142(18)
The Equilibrium Constant in Terms of Partition Functions
142(2)
Examples of the Calculation of Equilibrium Constants
144(7)
Thermodynamic Tables
151(9)
Quantum Statistics
160(34)
A Weakly Degenerate Ideal Fermi-Dirac Gas
162(2)
A Strongly Degenerate Ideal Fermi-Dirac Gas
164(5)
A Weakly Degenerate Ideal Bose-Einstein Gas
169(2)
A Strongly Degenerate Ideal Bose-Einstein Gas
171(6)
An Ideal Gas of Photons (Blackbody Radiation)
177(5)
The Density Matrix
182(3)
The Classical Limit from the Quantum Mechanical Expression for Q
185(9)
Crystals
194(28)
The Vibrational Spectrum of a Monatomic Crystal
194(3)
The Einstein Theory of the Specific Heat of Crystals
197(3)
The Debye Theory of the Heat Capacity of Crystals
200(6)
Introduction to Lattice Dynamics
206(6)
Phonons
212(2)
Point Defects in Solids
214(8)
Imperfect Gases
222(32)
The Virial Equation of State from the Grand Partition Function
224(2)
Virial Coefficients in the Classical Limit
226(7)
Second Virial Coefficient
233(4)
Third Virial Coefficient
237(2)
Higher Virial Coefficients for the Hard-Sphere Potential
239(2)
Quantum Corrections to B2(T)
241(2)
The Law of Corresponding States
243(2)
Conclusion
245(9)
Distribution Functions in Classical Monatomic Liquids
254(46)
Introduction
255(2)
Distribution Functions
257(4)
Relation of Thermodynamic Functions to g(r)
261(3)
The Kirkwood Integral Equation for g(r)
264(4)
The Direct Correlation Function
268(2)
Density Expansions of the Various Distribution Functions
270(4)
Derivation of Two Additional Integral Equations
274(3)
Density Expansions of the Various Integral Equations
277(2)
Comparisons of the Integral Equations to Experimental Data
279(21)
Perturbation Theories of Liquids
300(26)
Statistical Mechanical Perturbation Theory
302(2)
The van der Waals Equation
304(2)
Several Perturbation Theories of Liquids
306(20)
Solutions of Strong Electrolytes
326(31)
The Debye-Huckel Theory
328(12)
Some Statistical Mechanical Theories of Ionic Solutions
340(17)
Kinetic Theory of Gases and Molecular Collisions
357(22)
Elementary Kinetic Theory of Transport in Gases
358(7)
Classical Mechanics and Molecular Collisions
365(5)
Mean-Square Momentum Change During a Collision
370(9)
Continuum Mechanics
379(23)
Derivation of the Continuity Equations
380(6)
Some Applications of the Fundamental Equations of continuum Mechanics
386(5)
The Navier--Stokes Equations and Its Solution
391(11)
Kinetic Theory of Gases and the Boltzmann Equation
402(24)
Phase Space and the Liouville Equation
402(3)
Reduced Distribution Functions
405(1)
Fluxes in Dilute Gases
406(3)
The Boltzmann Equation
409(2)
Some General Consequences of the Boltzmann Equation
411(15)
Transport Processes in Dilute Gases
426(26)
Outline of the Chapman--Enskog Method
426(4)
Summary of Formulas
430(3)
Transport Coefficients for Various Intermolecular Potentials
433(7)
Extensions of the Boltzmann Equation
440(12)
Theory of Brownian Motion
452(15)
The Langevin Equation
452(4)
The Fokker--Planck Equation and the Chandrasekhar Equation
456(11)
The Time-Correlation Function Formalism, I
467(76)
Absorption of Radiation
470(6)
Classical Theory of Light Scattering
476(8)
Raman Light Scattering
484(5)
An Elementary Derivation of the Basic Formulas
489(6)
Dielectric Relaxation
495(4)
Time-Correlation Function Formalism of Molecular Spectroscopy
499(8)
Derivation of the Basic Formulas from the Liouville Equation
507(5)
Time-Correlation Function Expressions for the Thermal Transport Coefficients
512(10)
Applications of the Time-Correlation Function Formulas for the Thermal Transport Coefficients
522(21)
The Time-Correlation Function Formalism, II
543(50)
Inelastic Neutron Scattering
544(9)
The Weiner--Khintchine Theorem
553(8)
Laser Light Scattering
561(11)
The Memory Function
572(7)
Derivation of Thermal Transport Coefficients
579(14)
Appendix A Values of Some Physical Constants and Energy Conversion Factors 593(2)
Appendix B Fourier Integrals and the Dirac Delta Function 595(4)
Appendix C Debye Heat Capacity Function 599(1)
Appendix D Hard-Sphere Radial Distribution Function 600(4)
Appendix E Tables for the m-6-8 Potential 604(4)
Appendix F Derivation of the Golden Rule of Perturbations Theory 608(4)
Appendix G The Dirac Bra and Ket Notation 612(3)
Appendix H The Heisenberg Time-Dependent Representation 615(3)
Appendix I The Poynting Flux Vector 618(4)
Appendix J The Radiation Emitted By an Oscillating Dipole 622(4)
Appendix K Dielectric Constant and Absorption 626(5)
Index 631

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