[Volume. 1]----------
CONTENTS
Contents of volume 2 = ⅹ
Preface = xv
Chapter 1. INTRODUCTION
1.1 Atoms and Molecules = 2
1.2 Classical Mechanics = 3
1.3 Quantum Mechanics = 3
1.4 Macroscopic Properties. Thermodynamics = 4
1.5 Pressure. Kinetic Theory = 5
1.6 Equilibrium and Non-equilibrium = 7
References = 8
Chapter 2. PROBABILITIES AND STATISTICS. CORRELATED WALKS.
2.1 Probabilities = 10
2.2 Binomial Distribution = 13
2.3 Average and Root-Mean-Square Deviation. Random Walks = 18
2.4 Probability Density. Maxwell Velocity Distribution Function 1 = 23
2.5 Even and Odd Functions. Maxwell Velocity Distribution Function 2 = 29
2.6 Vacancy Diffusion. Correlated walks = 39
2.7 Solutions of Correlated Walks in One Dimension = 47
2.8 Correlated walks in Three Dimensions = 57
References = 59
Review Questions = 60
General Problems = 61
Chapter 3. LIOUVILLE'S THEOREM. FLUID DYNAMICS. NORMAL MODES OF OSCILLATION.
3.1 Newtonian, Lagrangian and Hamiltonian Descriptions of Linear Motion. = 64
3.2 State of Motion. Its Representation in Phase Space Reversible Motion = 73
3.3 Liouville's Theorem = 81
3.4 Hamiltonian Mechanics for a System of Many Particles = 87
3.5 Canonical Transformation = 94
3.6 Poisson Brackets = 100
3.7 Fluid Dynamics. Basic Evolution Equations = 107
3.8 Fluid Dynamics and Statistical Mechanics = 115
3.9 Oscillations of Particles on a String. Normal Modes = 120
3.10 Normal Coordinates = 128
3.11 Transverse Oscillations of a Stretched String = 133
3.12 Normal Coordinates for a String = 142
3.13 Velocity-Dependent Potential Generating the Lorentz Force = 153
References = 161
Review Questions = 162
General Problems = 163
Chapter 4. DISTRIBUTION FUNCTIONS. LIOUVILLE AND BOLTZMANN EQUATIONS
4.1 Irreversible Processes. Viscous Flow. Diffusion = 167
4.2 The Particle-Number Density. Microscopic Density = 174
4.3 Probability Distribution Function. The Liouville Equation = 184
4.4 The Gibbs Ensemble. The Liouville'Equation in the Γ-space = 192
4.5 More about the Liouville Equation = 197
4.6 The Many-Particle Distribution Function in the μ-Space. The Indistinguishability Factor = 200
4.7 Reduced Distribution Functions in the μ-Space = 211
4.8 Reduced Distribution Functions and Macroscopic Properties = 220
4.9 Evolution Equations for the Distribution Function f = 229
4.10 Rate of Collision. Mean Free Path = 235
4.11 Two Body Problem. Binary Collision = 240
4.12 The Boltzmann Equation = 253
4.13 Symmetries of Hamiltonians and Stationary States = 262
4.14 The Maxwell-Boltzmann Distribution Function = 269
4.15 Effusion. Experimental Check of the Velocity Distribution = 273
4.16 The H-theorem of Boltzmann = 281
4.17 Transport Coefficients = 285
References = 288
Review Questions = 290
General Problems = 291
Chapter 5 EQUATION OF STATE. FIRST AND SECOND LAWS OF THERMODYNAMICS
5.1 Equation of Thermodynamic State = 294
5.2 Ideal Gas. The absolute Temperature T = 295
5.3 Work. Quasi-static Processes. P-V Diagram = 297
5.4 Heat. Heat Capacities = 302
5.5 The First Law of Thermodynamics = 304
5.6 The First Law Applied to a Fluid = 306
5.7 Joule's Experment on the Free Expansion of a Gas = 309
5.8 Adiabatic Change of State = 313
5.9 The Second Law of Thermodynamics = 316
5.10 The Carnot Cycle = 318
5.11 Carnot's Theorem = 322
5.12 Heat Engines. Refrigerating Machines = 327
5.13 Vapor(Gas)-Liquid Transition. Critical State = 328
5.14 The Van der Waals Equation of State = 331
References = 337
Review Questions = 338
General Problems = 339
Chapter 6. ENTROPY. THERMODYNAMIC RELATIONS. APPLICATIONS
6.1 Clausius' Theorem = 342
6.2 The Entropy = 351
6.3 Some important Properties of the Entropy = 356
6.4 The perfect Differential = 361
6.5 Entropy of a Gas = 364
6.6 The Equation of Clausius and Clapeyron = 368
6.7 The Helmholtz Free Energy = 371
6.8 The Gibbs Free Energy = 375
6.9 Maxwell Relations = 379
6.10 Heat Capacities = 386
6.11 Sound Waves = 392
References = 397
Review Questions = 398
General Problems = 399
Chapter 7. CLASSICAL STATISTICAL MECHANICS. BASIC PRINCIPLES. SIMPLE APPLICATIONS
7.1 Fundamental Theorem. Canonical Ensemble = 402
7.2 More about the Canonical Ensemble. Approach to Stationary States = 406
7.3 Partition Function and Thermodynamic Quantities = 414
7.4 Classical Free Particles and an Ideal Gas = 420
7.5 Equipartition Theorem = 424
7.6 Heat Capacities of Simple Systems = 428
7.7 Fluctuation of Energy = 432
7.8 Bulk Limit = 434
7.9 The Entropy of Mixing = 440
7.10 The Gibbs Paradox = 446
7.11 Grand Canonical Ensemble = 448
7.12 Grand Partition Function and Thermodynamic Quantities = 455
References = 460
Review Questions = 461
General Problems = 462
APPENDICES
A. Integrals Involving Exponential and Gaussian Functions = 465
B. Arrival Probabilities in Correlated Walks = 467
C. Vectors 472
D. Tensors 490
E. The Representation-Independence of Poisson's Brackets = 497
F. Derivation of the B-B-G-K-Y Hierarchy Equation = 502
USEFUL PHYSICAL CONSTANTS = 505
MATHEMATICAL SIGNS AND SYMBOLS = 506
LIST OF SYMBOLS = 507
INDEX = 512
[Volume. 2]----------
CONTENTS
Contents of volume 1
Second Preface
Chapter 8. QUANTUM MECHANICS. FUNDAMENTALS REVIEWED
8.1 Basic Experimental Facts = 2
8.2 Generalized Vectors. Matrices = 7
8.3 Linear Operators = 15
8.4 The Eigenvalue Problem = 21
8.5 Orthogonal Representation = 26
8.6 Quantum Mechanical Despription of Linear Motion = 33
8.7 The Momentum Eigenvalue Problem = 41
8.8 The Energy Eigenvalue Problem = 47
8.9 Simple Harmonic Oscillator = 51
8.10 Heisenberg's Uncertainty Principle = 58
8.11 Particle Moving in Three-dimensional Space = 63
8.12 Free Particle in Space = 69
8.13 Five Fundamental Postulates in Quantum Mechanics = 75
8.14 The Heisenberg Picture = 81
8.15 Correspondence between Quantum and Classical Mechanics = 87
8.16 The Gibbs Ensemble in Quantum Mechanics = 91
References = 99
Review Questions = 100
General Problems = 101
Chapter 9. QUANTUM STATISTICAL MECHANICS. BASIC PRINCIPLES
9.1 Permutation Group = 105
9.2 Odd and Even Permutations = 107
9.3 Indistinguishable Classical Particles = 115
9.4 Quantum Statistical Postulate. Symmetric States for Bosons = 120
9.5 Antisymmetric States for Fermions. Pauli's Exclusion Principle = 123
9.6 More about Bosons and Fermions. Quantum Statistics and spin = 127
9.7 The Occupation Number Representation = 130
9.8 The Gibbs Ensemble of Many-Particle Systems The Caninical Ensemble = 134
9.9 The Partition Function = 138
9.10 The Grand Canonical Ensemble = 143
9.11 The Bose and Fermi Distribution Functions = 149
9.12 Quantum Statistics in the Classical Limit = 153
9.13 Applicability of Classical Statistical Mechanics = 163
References = 167
Review Questions = 168
General Problems = 169
Chapter 10. CONDUCTION ELECTRONS AND LIQUID HELIUM
10.1 Conduction Electrons in a Metal = 172
10.2 Free electrons. Fermi Energy = 177
10.3 The Density of State in Momentum Space = 184
10.4 The Density of States in Energy = 189
10.5 The Heat Capacity of Degenerate Electrons. Qualitative Discussions = 193
10.6 The Heat Capacity of Degenerate Electrons. Quantitative Calculations = 197
10.7 Liquid Helium = 204
10.8 Free Bosons. The Bose-Einstein Condensation = 206
10.9 Bosons in Condensed Phase = 211
References = 220
Review Questions = 220
General Problems = 221
Chapter 11. BLACK BODY RADIATION. LATTICE VIBRATIONS
11.1 Electric and Magnetic Fields in a Vacuum. The Wave Equation and its Plane-Wave Solution = 224
11.2 The Electromagnetic Field Energy. Canonical Transformation = 231
11.3 Black Body Radiation. Planck Distribution Function = 238
11.4 Experimental Verification of the Planck Distribution Function = 242
11.5 Radiation Pressure = 248
11.6 Crystal Lattices = 252
11.7 Lattice Vibrations. Einstein's Theory of the Heat Capacity = 255
11.8 Elastic Properties = 260
11.9 Elastic Waves = 264
11.10 The Hamiltonian for Elastic Waves = 269
11.11 Debye's Theory of the Heat Capacity = 277
11.12 More about the Heat Capacity. Lattice Dynamics = 290
References = 299
Review Questions = 300
General Problems = 301
Chapter 12. SPIN AND MAGNETISM. PHASE TRANSITIONS. POLYMER CONFORMATION
12.1 Angular Momentum in Quantum Mechanics = 304
12.2 Properties of Angular Momentum = 308
12.3 The Spin Angular Momentum = 314
12.4 The Spin of the Electron = 317
12.5 The Magnetogyric Ratio = 321
12.6 Paramagnetism of Isolated Atoms. Curie's Law = 328
12.7 Pauli Paramagnetism.(Paramagnetism of degenerate Electrons) = 335
12.8 Ferromagnetism. Internal Field Model(Weiss) = 339
12.9 The Ising Model. Solution of the One-Dimensional Model = 349
12.10 Braggs-Williams Approximation = 359
12.11 More about the Ising Model = 366
12.12 Conformation of Polymers in Dilute Solution = 379
12.13 Helix-Coil Transition of Polypeptides in Solution = 385
References = 399
Review Questions = 401
General Problems = 402
Chapter 13. TRANSPORT PHENOMENA
13.1 Ohm's Law. The Electrical Conductivity. Matthiessen's Rule = 405
13.2 The Boltzmann Equation for an Electron-Impurity System = 409
13.3 The Current Relaxation Rate. = 413
13.4 Applications to Semiconductors = 420
13.5 The Motion of a Charged Particle in an Electromagnetic Field = 429
13.6 Generalized Ohm's Law. Absorption Power = 437
13.7 Kubo's Formula for the Electrical Conductivity = 444
13.8 More about Kubo's Formula = 451
13.9 The Dynamic Condictivity of Free Electrons = 455
13.10 More about the Mobility. Quasi-Particle Effect = 462
13.11 The Cyclotron Resonance = 471
13.12 The Diffusion = 479
13.13 Simulation of the Lorentz Gas = 483
13.14 Atomic Diffusion in Metals with Impurities = 493
References = 501
Review Questions = 503
General Problems = 504
BIBLIOGRAPHY = 506
USEFUL PHYSICAL CONSTANT = 512
LIST OF SYMBOLS = 513
INDEX = 516
