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| Ïîèñê ïî óêàçàòåëÿì |
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| Walecka J.D. — Fundamentals of statistical mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
Invariance 71
Irreversible processes 69f 72
Isothermal processes 61f 69
Jacobian determinant 20 22 271—272
Jacobian determinant, canonical transformation and 97 259
Jacobian determinant, defined 16
Jacobian determinant, Poisson bracket and 261
Kelvin’s scale 60
Kronecker delta function 16 110
Langevin — Curie theory 154 156
Langevin’s formula 283
Lattice structure 133—135 138
Light, velocity of 140
Linear chain 116—125 132f
Linear chain, dispersion relation 123
Linear chain, fixed end-points 116—120 123
Linear chain, interatomic potential in 117
Linear chain, periodic boundary conditions 126 209
Linear chain, phase velocity 140
Linear chain, wavenumbers for 125f
Linear chain, with ends joined 126
Linearly independent solutions 126
Liouville’s theorem 15—23 34 70 272
Liouville’s theorem, alternate proofs of vi 36
Liouville’s theorem, Ehrenfest’s theorem and 171
Liouville’s theorem, general proof of 258—261
Liouville’s theorem, Hamilton’s equations and 36
Liouville’s theorem, quantum version of 169 283
Lorentz force 149
Macroscopic systems v 1 29 61 64 230
Magnetic dipole moment 145f
Magnetic fields 223
Magnetic fields, charged particles in 149
Magnetic fields, classical theory of magnetism 151
Magnetic fields, free energy 154 156
Magnetic fields, hamiltonian for 216
Magnetic fields, in a cavity 139—142 215
Magnetic fields, inhomogeneous 146
Magnetic fields, Langevin — Curie theory 154—156
Magnetic fields, magnetic moment 145—146 152f 218 282 287
Magnetic fields, partition function 152ff
Magnetic fields, quantum mechanical subsystem 216f (see also “Diamagnetism” “Ferromagnetism” “Paramagnetism”)
Magnetic fields, saturation value 156
Magnetic fields, susceptibility 145 154f
Magnetic fields, temperature and 154
Magneton 219
Mass points, motion of 3f 10 19
Matrix theory 159 162—166 175—177 “Eigenvalues” “Hermitian
Maxwell — Boltzmann distribution 80 236
Maxwell, J.C. 1
Maxwell’s equations 139—141
Mean energy 64f 95
Mean values 26—32
Mean values, equilibrium and 42f
Mean values, significance of 28
Mean values, stationary 40—42
Mean values, thermodynamic energy and 64
Mean values, time derivative and 42
Mean values, virial theorem and 94
Melting point 107 109
Micro-phase space 97 262
Microscopic systems v 61
Mixing, of states 180
Modulus, of ensembles 55
Molar specific heat 109f
Molecular distributions 33 262—264
Momentum-space integrals 76
Monatomic gases 74 84 193—196 224
Nearest neighbor interactions 116
Neg-entropy 68
Nernst theorem 109 189—192 196 285
Neutrons 219 226
Newton’s laws 4 6 11 84 86 146
Noble gases 155
Non-ideal gas 90
Normal coordinates 110—115 119 122 127f
Normal mode problem 119
Normalization, condition 112—113 180
Normalization, constants of 122 127—128 142 186
Normalization, ensembles and 168f
Normalization, hermitian operators and 162
Normalization, preserved in time 174
Observables, complete set 165
Observables, expectation value of 177
Observables, operators and 162f
Observables, statistical average 172
Occupation number 227f 232 238ff
One-particle partition function 75 220
Operators 159
Operators, degeneracy and 166
Operators, mutually commuting 165
Operators, product of 177 (see also “Matrix theory” “Specific
Orientation, atomic 153 155 220
Orthogonality 112
Orthogonalization 282
Orthonormal vectors 136
Orthonormality condition 112—113 121 127—128 160
Paramagnetism, defined 145
Paramagnetism, entropy and 283
Paramagnetism, magnetization and 221
Paramagnetism, partition function 155
Paramagnetism, quantum theory of 221f
Paramagnetism, susceptibility 154
Parity transformation 206n
Partition function 56 58 60—73 187 279
Partition function, canonical ensemble and 229
Partition function, classical vs.quantum 194 223—225 289
Partition function, entropy and 66
Partition function, factored 66 75
Partition function, for three-dimensional solid 209f
Partition function, free energy and 62 149
Partition function, high temperatures and 223—225 283
Partition function, internal 98 152f 220
Partition function, magnetic fields and 148—149 152f
Partition function, of rigid rotor 99
Partition function, one-particle 75 194f
Partition function, paramagnetism and 155
Partition function, rotational degrees of freedom 286
Partition function, single particle 196
Partition function, thermodynamic functions and 187f
Partition function, vibrational 103
Pauli exclusion principle 228
Periodic boundary conditions 126—133 140 282
Perturbation theory 180
Phase density, as constant of motion 43
Phase density, equilibrium and 43
Phase density, hamiltonian and 44
Phase density, probability density and 54
Phase density, time dependence of 33—39
Phase extension 63—65 68 71
Phase extension, Boltzmann’s constant and 68
Phase extension, energy surfaces and 63
Phase extension, entropy and 68 70
Phase extension, finegrain description 71
Phase extension, information and 69
Phase extension, irreversible process and 70
Phase extension, Liouville’s theorem and 70 71
Phase extension, probability distribution and 64
Phase orbits 14f 169 274
Phase orbits, degeneracy and 180f
Phase orbits, distribution function 171
Phase orbits, energy surface and 4 47ff
Phase orbits, Hamilton’s equations and 47
Phase orbits, initial values 47
Phase orbits, phase density and 45
Phase space 14ff 17 75 258
Phase space, area in 22
Phase space, canonical ensemble 62
Phase space, coarse-grain average 49f 225
Phase space, density function 35
| Phase space, energy surface 63 73
Phase space, ensemble in 25
Phase space, micro-phase space 75 262
Phase space, quantum 168
Phase space, time evolution in 34
Phase space, volume element 66 81 149 258
Phase transition 247
phase velocity 132f
Phase velocity, linear chain 140
Phase velocity, running waves and 137
Phase volume 19 21 23 70
Planck distribution 144 198 210 216f
Planck, Max 2
Planck’s constant 105
Plane waves 120 140 195
Point transformations 9
Poisson brackets 37f
Poisson brackets, canonical transformations and 251—257
Poisson brackets, computation of 38
Poisson brackets, equilibrium and 43
Poisson brackets, invariance of 254—255
Poisson brackets, jacobian and 261
Polar coordinates 10 76 172f 182
Positive definite forms 108
Potential, hamiltonian and 5
Potential, interatomic 117—120
Potential, parabolic approximation 102
Potential, quadratic approximation 200
Potential, Taylor series and 102
Potential, thermal contact and 52
Potential, transverse vector 140
Probability density, canonical ensemble and 79 87 186f
Probability density, coarse-grain samples and 49
Probability density, density matrix 162—164 172—176 182—187 systems”)
Probability density, distribution function and 24—26
Probability density, entropy and 62f
Probability density, quantum mechanics and 157—159
Probability density, work and 57
Protons 219 226
Quadratic approximation 118 120
Quantum effects 191
Quantum grand partition function 231f
Quantum grand partition function, Bose statistics 243—247
Quantum grand partition function, Fermi statistics 233—242
quantum mechanics 157ff
Quantum numbers 167 194 201
Quantum partition function 187f 194 224 228
Quantum phase space 168 170
Quasi-ergodic systems 45—49 180 275
Rayleigh — Jeans law 144 216
Reciprocal lattice 135f 142
Relativistic quantum theory 226
Relativity theory 6f
Reversible processes 42 57 61 69
Rigid rotor 99 204
Root-mean-square deviation 27 29
Rotational energy 286
Rotational energy, degrees of freedom and 106
Rotational energy, freezing out of 205
Rotational energy, hamiltonian for 100 200f
Rotational energy, of diatomic molecule 204 285
Rotational energy, partition function for 204
Rotational energy, rigid 98ff 204
Rotational energy, spectrum of 204
Running waves 129 132 134 137
Sackur — Tetrode equation 285
Schmidt procedure 112 282
Schrodinger equation 284
Schrodinger equation, rotation from 169
Schrodinger equation, time-dependent 159 160—161
Self-force 86
Semi-permeable membranes 234
Solids 106—137
Solids, contact surface 32
Solids, crystals 106f 110 133—135 138
Solids, Debye theory 210—214
Solids, energy of 211
Solids, specific heat of 209—214
Solids, three-dimensional 133
Sound waves 133 137 210
Specific heat 106 109 208 277 280 282
Specific heat, Debye theory 213f 224 240
Specific heat, harmonic oscillators and 281
Specific heat, low-temperature 214
Specific heat, of solids 209—214
Specific heat, quantum paradox 138
Spherical coordinates 10 97 203 281
Spherical harmonics 203 206
Spin system 206 218 226 283 292
Spin-degeneracy factor 235
Spring constant 103
standing waves 129
State functions see “Thermodynamic functions” “Thermodynamic(s)”
Stationary mean values 40—42
Stationary states 160
Statistical density matrix see “Density matrix”
Statistical density operator 183 187
Statistical ensembles 24—39 164—173
Stefan — Boltzmann constant 215
Stirling’s formula 278n
Strong field approximation 288
Surface effects 33
Symmetry of wavefunction 206 226 228
Symmetry, irreversibility and 69—72
Taylor series expansion 102
Temperature, concept of 51 53 55 60 188f
Thermal equilibrium 40—73 177—185 264 276
Thermal equilibrium, canonical distributions and 50—55
Thermal equilibrium, conditions of 42—43
Thermal equilibrium, coupling and 186f
Thermal equilibrium, defined 42
Thermal equilibrium, entropy and 60—68
Thermal equilibrium, mean values and 42—43
Thermal equilibrium, mutual 231f (see also “Specific systems”)
Thermal equilibrium, of black bodies 139
Thermal equilibrium, partition function 61—73
Thermal equilibrium, phase density and 43
Thermal equilibrium, Poisson bracket and 43
Thermal equilibrium, reversible changes 57
Thermal equilibrium, small oscillations and 209
Thermal equilibrium, stationary mean values and 40—50
Thermal equilibrium, statistical density matrix 177
Thermal equilibrium, systems in 45
Thermal equilibrium, temperature of 51 53
Thermal equilibrium, thermodynamic functions and 55—61
Thermodynamic potential 291
Thermodynamic processes 147 188
Thermodynamic(s) 2 12
Thermodynamic(s), first law of 55f 188
Thermodynamic(s), second law of 58 188 “Specific systems”)
Thermodynamic(s), statistical mechanics and 44 61
Thermodynamic(s), thermodynamic functions 55—60 187—190
Thermodynamical variables 29 42
Thomson, William 1
Time dependence 9n 34 43 45 174
Time derivative 20n 42
Time, entropy and 72
Time-reversal transformation 71
Trace, invariance of 164
Translational motion, freezing out 197
Transverse potential 140
Ultraviolet catastrophe 142 144
Uncertainty principle 157—159
Unitarity 169
Van der Waal’s equation 89—91
van Leeuwen’s theorem 150
Variational Principle 7f
Vector field 133
Vector potential 140 142 148ff
Vibrational energy 99—105
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