Statistical Mechanics

, by McQuarrie, Donald A.

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ISBN: 9781891389153 | 1891389157
Cover: Hardcover
Copyright: 2/1/2000

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Preface

Introduction and Review

(34)

Introduction

(2)

Classical Mechanics

(5)

Quantum mechanics

(5)

Thermodynamics

(7)

Mathematics

(15)

The Canonical Ensemble

(16)

Ensemble Averages

(2)

Method of the Most Probable Distribution

(3)

The Evaluation of the Undetermined Multipliers, α and β

(4)

Thermodynamic Connection

(7)

Other Ensemble and Fluctuations

(17)

Grand canonical Ensemble

(4)

Other Ensembles

(2)

Fluctuations

(11)

Boltzmann Statistics, Fermi-Dirac Statistics, and Bose-Einstein Statistics

(13)

The Special Case of Boltzmann Statistics

(5)

Fermi-Dirac and Bose-Einstein Statistics

(8)

Ideal Monatomic Gas

(10)

The Translational Partition Function

(2)

The Electronic and Nuclear Partition Functions

(2)

Thermodynamic Functions

(2)

A Digression on Atomic Term Symbols

(4)

Ideal Diatomic Gas

(22)

The Rigid Rotor-Harmonic Oscillator Approximation

(5)

The Vibrational Partition Function

(2)

The Rotational Partition Function of a Heteronuclear Diatomic Molecule

(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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Table of Contents

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