Course of Theoretical Physics

Preface to the Third Russian Edition From the Prefaces to Previous Russian Editions Notation I. The Fundamental Principles of Statistical Physics § 1. Statistical Distributions § 2. Statistical Independence § 3. Liouville's Theorem § 4. The Significance of Energy § 5. The Statistical Matrix § 6. Statistical Distributions in Quantum Statistics § 7. Entropy § 8. The Law of Increase of Entropy II. Thermodynamic Quantities § 9. Temperature § 10. Macroscopic Motion § 11. Adiabatic Processes § 12. Pressure § 13. Work and Quantity of Heat § 14. The Heat Function § 15. The Free Energy and the Thermodynamic Potential § 16. Relations Between the Derivatives of Thermodynamic Quantities § 17. The Thermodynamic Scale of Temperature § 18. The Joule-Thomson Process § 19. Maximum Work § 20. Maximum Work Done by a Body in an External Medium § 21. Thermodynamic Inequalities § 22. Le Chatelier's Principle § 23. Nernst's Theorem § 24. The Dependence of the Thermodynamic Quantities on the Number of Particles § 25. Equilibrium of a Body in an External Field § 26. Rotating Bodies § 27. Thermodynamic Relations in the Relativistic Region III. The Gibbs Distribution § 28. The Gibbs Distribution § 29. The Maxwellian Distribution § 30. The Probability Distribution for an Oscillator § 31. The Free Energy in the Gibbs Distribution § 32. Thermodynamic Perturbation Theory § 33. Expansion in Powers of h § 34. The Gibbs Distribution for Rotating Bodies § 35. The Gibbs Distribution for a Variable Number of Particles § 36. The Derivation of the Thermodynamic Relations from the Gibbs Distribution IV. Ideal Gases § 37. The Boltzmann Distribution § 38. The Boltzmann Distribution in Classical Statistics § 39. Molecular Collisions § 40. Ideal Gases Not in Equilibrium § 41. The Free Energy of an Ideal Boltzmann Gas § 42. The Equation of State of an Ideal Gas § 43. Ideal Gases With Constant Specific Heat § 44. The Law of Equipartition § 45. Monatomic Ideal Gases § 46. Monatomic Gases. The Effect of the Electronic Angular Momentum § 47. Diatomic Gases With Molecules of Unlike Atoms. Rotation of Molecules § 48. Diatomic Gases With Molecules of Like Atoms. Rotation of Molecules § 49. Diatomic Gases. Vibrations of Atoms § 50. Diatomic Gases. The Effect of the Electronic Angular Momentum § 51. Polyatomic Gases § 52. Magnetism of Gases V. The Fermi and Bose Distributions § 53. The Fermi Distribution § 54. The Bose Distribution § 55. Fermi and Bose Gases Not in Equilibrium § 56. Fermi and Bose Gases of Elementary Particles § 57. A Degenerate Electron Gas § 58. The Specific Heat of a Degenerate Electron Gas § 59. Magnetism of an Electron Gas. Weak Fields § 60. Magnetism of an Electron Gas. Strong Fields § 61. A Relativistic Degenerate Electron Gas § 62. A Degenerate Bose Gas § 63. Black-Body Radiation VI. Solids § 64. Solids at Low Temperatures § 65. Solids at High Temperatures § 66. Debye's Interpolation Formula § 67. Thermal Expansion of Solids § 68. Highly Anisotropic Crystals § 69. Crystal Lattice Vibrations § 70. Number Density of Vibrations § 71. Phonons § 72. Phonon Creation and Annihilation Operators § 73. Negative Temperatures VII. Non-Ideal Gases § 74. Deviations of Gases from the Ideal State § 75. Expansion in Powers of the Density § 76. Van Der Waals' Formula § 77. Relationship of the Virial Coefficient and the Scattering Amplitude § 78. Thermodynamic Quantities for a Classical Plasma § 79. The Method of Correlation Functions § 80. Thermodynamic Quantities for a Degenerate Plasma VIII. Phase Equilibrium § 81. Conditions of Phase Equilibrium § 82. The Clapeyron-Clausius Formula § 83. The Critical Point § 84. The Law of Corresponding States IX. Solutions § 85. Systems Containing Different Particles § 86. The Phase Rule § 87. Weak Solutions § 88. Osmotic Pressure § 89. Solvent Phases in Contact § 90. Equilibrium With Respect To the Solute § 91. Evolution of Heat and Change of Volume on Dissolution § 92. Solutions of Strong Electrolytes § 93. Mixtures of Ideal Gases § 94. Mixtures of Isotopes § 95. Vapor Pressure Over Concentrated Solutions § 96. Thermodynamic Inequalities for Solutions § 97. Equilibrium Curves § 98. Examples of Phase Diagrams § 99. Intersection of Singular Curves on the Equilibrium Surface § 100. Gases and Liquids X. Chemical Reactions § 101. The Condition for Chemical Equilibrium § 102. The Law of Mass Action § 103. Heat of Reaction § 104. Ionization Equilibrium § 105. Equilibrium With Respect To Pair Production XI. Properties of Matter at Very High Density § 106. The Equation of State of Matter at High Density § 107. Equilibrium of Bodies of Large Mass § 108. The Energy of a Gravitating Body § 109. Equilibrium of a Neutron Sphere XII. Fluctuations § 110. The Gaussian Distribution § 111. The Gaussian Distribution for More Than One Variable § 112. Fluctuations of the Fundamental Thermodynamic Quantities § 113. Fluctuations in an Ideal Gas § 114. Poisson's Formula § 115. Fluctuations in Solutions § 116. Spatial Correlation of Density Fluctuations § 117. Correlation of Density Fluctuations in a Degenerate Gas § 118. Correlations of Fluctuations in Time § 119. Time Correlations of the Fluctuations of More Than One Variable § 120. The Symmetry of the Kinetic Coefficients § 121. The Dissipative Function § 122. Spectral Resolution of Fluctuations § 123. The Generalized Susceptibility § 124. The Fluctuation-Dissipation Theorem § 125. The Fluctuation-Dissipation Theorem for More Than One Variable § 126. The Operator Form of the Generalized Susceptibility § 127. Fluctuations in the Curvature of Long Molecules XIII. The Symmetry of Crystals § 128. Symmetry Elements of a Crystal Lattice § 129. The Bravais Lattice § 130. Crystal Systems § 131. Crystal Classes § 132. Space Groups § 133. The Reciprocal Lattice § 134. Irreducible Representations of Space Groups § 135. Symmetry Under Time Reversal § 136. Symmetry Properties of Normal Vibrations of a Crystal Lattice § 137. Structures Periodic in One and Two Dimensions § 138. The Correlation Function in Two-Dimensional Systems § 139. Symmetry With Respect To Orientation of Molecules § 140. Nematic and Cholesteric Liquid Crystals § 141. Fluctuations in Liquid Crystals XIV. Phase Transitions of the Second Kind and Critical Phenomena § 142. Phase Transitions of the Second Kind § 143. The Discontinuity of Specific Heat § 144. Effect of an External Field on a Phase Transition § 145. Change in Symmetry in a Phase Transition of the Second Kind § 146. Fluctuations of the Order Parameter § 147. The Effective Hamiltonian § 148. Critical Indices § 149. Scale Invariance § 150. Isolated and Critical Points of Continuous Transition §151. Phase Transitions of the Second Kind in a Two-Dimensional Lattice § 152. Van Der Waals Theory of the Critical Point § 153. Fluctuation Theory of the Critical Point XV. Surfaces § 154. Surface Tension § 155. Surface Tension of Crystals § 156. Surface Pressure § 157. Surface Tension of Solutions § 158. Surface Tension of Solutions of Strong Electrolytes § 159. Adsorption § 160. Wetting § 161. The Angle of Contact § 162. Nucleation in Phase Transitions § 163. The Impossibility of the Existence of Phases in One-Dimensional SystemsIndexContents of Part 2 PrefaceNotationI. The Normal Fermi Liquid § 1. Elementary Excitations in a Quantum Fermi Liquid § 2. Interaction of Quasi-Particles § 3. Magnetic Susceptibility of a Fermi Liquid § 4. Zero Sound § 5. Spin Waves in a Fermi Liquid § 6. A Degenerate Almost Ideal Fermi Gas With Repulsion Between the ParticlesII. Green's Functions in a Fermi System at T = O § 7. Green's Functions in a Macroscopic System § 8. Determination of the Energy Spectrum from the Green's Function § 9. Green's Function of an Ideal Fermi Gas § 10. Particle Momentum Distribution in a Fermi Liquid § 11. Calculation of Thermodynamic Quantities from the Green's Function § 12. Ø Operators in the Interaction Representation § 13. The Diagram Technique for Fermi Systems § 14. The Self-Energy Function § 15. The Two-Particle Green's Function § 16. The Relation of the Vertex Function To the Quasi-Particle Scattering Amplitude § 17. The Vertex Function for Small Momentum Transfers § 18. The Relation of the Vertex Function To the Quasi-Particle Interaction Function § 19. Identities for Derivatives of the Green's Function § 20. Derivation of the Relation Between the Limiting Momentum and the Density § 21. Green's Function of an Almost Ideal Fermi GasIII. Superfluidity § 22. Elementary Excitations in a Quantum Bose Liquid § 23. Superfluidity § 24. Phonons in a Liquid § 25. A Degenerate Almost Ideal Bose Gas § 26. The Wave Function of the Condensate § 27. Temperature Dependence of the Condensate Density § 28. Behavior of the Superfluid Density Near the λ-Point § 29. Quantized Vortex Filaments § 30. A Vortex Filament in an Almost Ideal Bose Gas § 31. Green's Functions in a Bose Liquid § 32. The Diagram Technique for a Bose Liquid § 33. Self-Energy Functions § 34. Disintegration of Quasi-Particles § 35. Properties of the Spectrum Near Its Termination PointIV. Green's Functions at Non-Zero Temperatures § 36. Green's Functions at Non-Zero Temperatures § 37. Temperature Green's Functions § 38. The Diagram Technique for Temperature Green's FunctionsV. Superconductivity § 39. A Superfluid Fermi Gas. The Energy Spectrum § 40. A Superfluid Fermi Gas. Thermodynamic Properties § 41. Green's Functions in a Superfluid Fermi Gas § 42. Temperature Green's Functions in a Superfluid Fermi Gas § 43. Superconductivity in Metals § 44. The Superconductivity Current § 45. The Ginzburg-Landau Equations § 46. Surface Tension at the Boundary of Superconducting and Normal Phases § 47. The Two Types of Superconductor § 48. The Structure of the Mixed State § 49. Diamagnetic Susceptibility Above the Transition Point § 50. The Josephson Effect § 51. Relation Between Current and Magnetic Field in a Superconductor § 52. Depth of Penetration of a Magnetic Field Into a Superconductor § 53. Superconducting Alloys § 54. The Cooper Effect for Non-Zero Orbital Angular Momenta of the PairVI. Electrons in the Crystal Lattice § 55. an Electron in a Periodic Field § 56. Effect of an External Field on Electron Motion in a Lattice § 57. Quasi-Classical Trajectories § 58. Quasi-Classical Energy Levels § 59. The Electron Effective Mass Tensor in the Lattice § 60. Symmetry of Electron States in a Lattice in a Magnetic Field § 61. Electron Spectra of Normal Metals § 62. Green's Function of Electrons in a Metal § 63. The De Haas-Van Alphen Effect § 64. Electron-Phonon Interaction § 65. Effect of Electron-Phonon Interaction on the Electron Spectrum in a Metal § 66. The Electron Spectrum of Solid Insulators § 67. Electrons and Holes in Semiconductors § 68. The Electron Spectrum Near the Degeneracy PointVII. Magnetism § 69. Equation of Motion of the Magnetic Moment in a Ferromagnet § 70. Magnons in a Ferromagnet. The Spectrum § 71. Magnons in a Ferromagnet. Thermodynamic Quantities § 72. The Spin Hamiltonian § 73. Interaction of Magnons § 74. Magnons in an AntiferromagnetVIII. Electromagnetic Fluctuations § 75. Green's Function of a Photon in a Medium § 76. Electromagnetic Field Fluctuations § 77. Electromagnetic Fluctuations in an Infinite Medium § 78. Current Fluctuations in Linear Circuits § 79. Temperature Green's Function of a Photon in a Medium § 80. The Van Der Waals Stress Tensor § 81. Forces of Molecular Interaction Between Solid Bodies. The General Formula § 82. Forces of Molecular Interaction Between Solid Bodies. Limiting Cases § 83. Asymptotic Behavior of the Correlation Function in a Liquid § 84. Operator Expression for the Permittivity § 85. A Degenerate PlasmaIX. Hydrodynamic Fluctuations § 86. Dynamic Form Factor of a Liquid § 87. Summation Rules for the Form Factor § 88. Hydrodynamic Fluctuations § 89. Hydrodynamic Fluctuations in an Infinite Medium § 90. Operator Expressions for the Transport Coefficients § 91. Dynamic Form Factor of a Fermi LiquidIndex