Statistical Mechanics

by McQuarrie, Donald A.

• ISBN13: 9781891389153
• ISBN10: 1891389157
• Format: Hardcover
• Copyright: 2000-02-01
• Publisher: Univ Science Books

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