Elements of Statistical Mechanics, 3rd edition

✍ Scribed by D. ter Haar

• Year: 1995
• Tongue: English
• Leaves: 417
• Edition: 3
• Category: Library

✦ Synopsis

Following the Boltzmann-Gibbs approach to statistical mechanics, this new edition of Dr ter Haar's important textbook, Elements of Statistical Mechanics, provides undergraduates and more senior academics with a thorough introduction to the subject. Each chapter is followed by a problem section and detailed bibliography. The first six chapters of the book provide a thorough introduction to the basic methods of statistical mechanics and indeed the first four may be used as an introductory course in themselves. The last three chapters offer more detail on the equation of state, with special emphasis on the van der Waals gas; the second-quantisation approach to many-body systems, with an examination of two-time temperature-dependent Green functions; phase transitions, including various approximation methods for treating the Ising model, a brief discussion of the exact solution of the two-dimensional square Ising model, and short introductions to renormalisation group methods and the Yang and Lee theory of phase transitions. In the problem section which follows each chapter the reader is asked to complete proofs of basic theory and to apply that theory to various physical situations. Each chapter bibliography includes papers which are of historical interest. A further help to the reader are the solutions to selected problems which appear at the end of the book.

✦ Table of Contents

Front Cover......Page 1
Elements of Statistical Mechanics......Page 4
Copyright Page......Page 5
Table of Contents......Page 6
Preface to the third edition......Page 10
Preface to the second edition......Page 12
Preface to the first edition......Page 14
1.1. The Maxwell distribution......Page 16
1.2. The perfect gas law......Page 19
1.3. The van der Wads law......Page 22
1.4. Collisions......Page 26
1.5. The H-theorem......Page 34
1.6. The connection between H and entropy......Page 39
1.7. The connection between H and probability......Page 41
Problems......Page 44
Bibliographical notes......Page 47
2.1. The barometer formula......Page 51
2.2. The μ–
space......Page 53
2.4. Applications of the Maxwell-Boltzmann formula......Page 56
2.5. The Boltzmann transport equation......Page 61
2.6. External parameters......Page 63
2.7. The phase integral; connection with thermodynamics......Page 64
Problems
......Page 67
Bibliographical notes......Page 72
3.1. The partition function......Page 74
3.2. The harmonic oscillator......Page 76
3.3. Planck's radiation law......Page 82
3.4. The transition to classical statistics
......Page 86
3.5. The rigid rotator: the hydrogen molecule......Page 92
Problems......Page 96
Bibliographical notes......Page 100
4.1. Deviations from Boltzmann statistics......Page 103
4.2. The probability aspect of statistics......Page 105
4.3. The elementary method of statistics......Page 112
4.4. Connection with thermodynamics......Page 115
4.5. The Darwin-Fowler method......Page 119
4.6. The perfect Boltzmann gas......Page 126
4.7. The perfect Bose-Einstein gas......Page 129
4.8. The perfect Fermi-Dirac gas......Page 139
4.9. Are all particles bosons or fermions?......Page 146
Problems......Page 151
Bibliographical notes......Page 159
5.1. The Γ–space; ensembles......Page 162
5.2. Stationary ensembles......Page 170
5.3. The macrocanonical ensemble......Page 173
5.4. Fluctuations in a macrocanonical ensemble......Page 177
5.5. The entropy in a macrocanonical ensemble......Page 179
5.6. The coupling of two macrocanonical ensembles......Page 184
5.7. Microcanonical ensembles......Page 189
5.8. Application: the perfect gas......Page 192
5.9. Grand ensembles......Page 194
5.10. Fluctuations in a canonical grand ensemble......Page 199
5.11. The coupling of two canonical grand ensembles......Page 208
5.12. Application of the theory of classical grand ensembles to a perfect gas......Page 211
5.13. The relationship between ensembles and actually observed systems......Page 214
5.14. Ergodic theory snd the H-theorem in ensemble theory
......Page 219
Problems......Page 225
Bibliographical notes......Page 228
6.1. The density matrix......Page 231
6.2. Pure case and mixed case......Page 236
6.3. Macrocanonical ensembles in quantum statistics......Page 239
6.4. Canonical grand ensembles in quantum statistics......Page 242
6.5. The H-theorem in quantum statistics......Page 249
6.6. The perfect Boltzmann gas......Page 254
6.7. The perfect Bose-Einstein gas......Page 257
6.8. The perfect Fermi-Dirac gas......Page 261
6.9. The Saha equilibrium......Page 263
6.10. The relativistic electron gas......Page 265
Problems......Page 274
Bibliographical notes......Page 280
7.1. The equation of state......Page 283
7.2. The van der Waals equation of state......Page 289
Problems......Page 299
Bibliographical notes......Page 301
8.1. Quasi-particles and elementary excitations......Page 303
8.2. The occupation number representation for bosons......Page 309
8.3 The occupation number representation for fermions......Page 315
8.4. The Green function method in statistical mechanics......Page 316
Problems......Page 326
Bibliographical notes......Page 328
9.1. Introduction......Page 330
9.2. The liquid drop model of condensation......Page 333
9.3. Mayer’s theory of condensation......Page 338
9.4. Yang and Lee’s theory of phase transitions......Page 343
9.5. The Ising model of ferromagnetism......Page 350
9.6. The mean-field approximation......Page 357
9.7. The quasi-chemical approximation......Page 362
9.8. Critical phenomena......Page 365
9.9. Some exact results......Page 376
Problems......Page 382
Bibliographical notes......Page 386
Solutions to Selected Problems......Page 390
Index......Page 410