Elements of Statistical Mechanics (eBook)

Front Cover 1
Elements of Statistical Mechanics 4
Copyright Page 5
Table of Contents 6
Preface to the third edition 10
Preface to the second edition 12
Preface to the first edition 14
Chapter 1. The Maxwell distribution 16
1.1. The Maxwell distribution 16
1.2. The perfect gas law 19
1.3. The van der Wads law 22
1.4. Collisions 26
1.5. The H-theorem 34
1.6. The connection between H and entropy 39
1.7. The connection between H and probability 41
Problems 44
Bibliographical notes 47
Chapter 2. The Maxwell-Boltzmann distribution 51
2.1. The barometer formula 51
2.2. The ?–space 53
2.3. The H-theorem H and probability
2.4. Applications of the Maxwell-Boltzmann formula 56
2.5. The Boltzmann transport equation 61
2.6. External parameters 63
2.7. The phase integral connection with thermodynamics
Problems 67
Bibliographical notes 72
Chapter 3. The partition function 74
3.1. The partition function 74
3.2. The harmonic oscillator 76
3.3. Planck's radiation law 82
3.4. The transition to classical statistics 86
3.5. The rigid rotator: the hydrogen molecule 92
Problems 96
Bibliographical notes 100
Chapter 4. Bose-Einstein and Fermi-Dirac statistics 103
4.1. Deviations from Boltzmann statistics 103
4.2. The probability aspect of statistics 105
4.3. The elementary method of statistics 112
4.4. Connection with thermodynamics 115
4.5. The Darwin-Fowler method 119
4.6. The perfect Boltzmann gas 126
4.7. The perfect Bose-Einstein gas 129
4.8. The perfect Fermi-Dirac gas 139
4.9. Are all particles bosons or fermions? 146
Problems 151
Bibliographical notes 159
Chapter 5. Classical ensembles 162
5.1. The ?–space ensembles
5.2. Stationary ensembles 170
5.3. The macrocanonical ensemble 173
5.4. Fluctuations in a macrocanonical ensemble 177
5.5. The entropy in a macrocanonical ensemble 179
5.6. The coupling of two macrocanonical ensembles 184
5.7. Microcanonical ensembles 189
5.8. Application: the perfect gas 192
5.9. Grand ensembles 194
5.10. Fluctuations in a canonical grand ensemble 199
5.11. The coupling of two canonical grand ensembles 208
5.12. Application of the theory of classical grand ensembles to a perfect gas 211
5.13. The relationship between ensembles and actually observed systems 214
5.14. Ergodic theory snd the H-theorem in ensemble theory 219
Problems 225
Bibliographical notes 228
Chapter 6. The ensembles in quantum statistics 231
6.1. The density matrix 231
6.2. Pure case and mixed case 236
6.3. Macrocanonical ensembles in quantum statistics 239
6.4. Canonical grand ensembles in quantum statistics 242
6.5. The H-theorem in quantum statistics 249
6.6. The perfect Boltzmann gas 254
6.7. The perfect Bose-Einstein gas 257
6.8. The perfect Fermi-Dirac gas 261
6.9. The Saha equilibrium 263
6.10. The relativistic electron gas 265
Problems 274
Bibliographical notes 280
Chapter 7. The equation of state of an imperfect gas 283
7.1. The equation of state 283
7.2. The van der Waals equation of state 289
Problems 299
Bibliographical notes 301
Chapter 8. The occupation number representation 303
8.1. Quasi-particles and elementary excitations 303
8.2. The occupation number representation for bosons 309
8.3 The occupation number representation for fermions 315
8.4. The Green function method in statistical mechanics 316
Problems 326
Bibliographical notes 328
Chapter 9. Phase transitions 330
9.1. Introduction 330
9.2. The liquid drop model of condensation 333
9.3. Mayer’s theory of condensation 338
9.4. Yang and Lee’s theory of phase transitions 343
9.5. The Ising model of ferromagnetism 350
9.6. The mean-field approximation 357
9.7. The quasi-chemical approximation 362
9.8. Critical phenomena 365
9.9. Some exact results 376
Problems 382
Bibliographical notes 386
Solutions to Selected Problems 390
Index 410