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| Walecka J.D. — Fundamentals of statistical mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
Absolute temperature 58
Absolute zero 189
Additive property 30—32 262
Antisymmetry 206 226 228
Atoms, Bohr radius 152
Atoms, crystal structures 106—107
Atoms, dipolar interaction 282 (see also “Specific particles parameters structures”)
Atoms, distances in 212
Atoms, equilibrium position 107
Atoms, interatomic potential 96 116 118—119
Atoms, magnetic moment of 151f
Atoms, orientation of 153
Avogadro’s number v 60 279
Basis of solutions 127 160
Bernoulli, Daniel 1
Binding energy 101 118
Binomial theorem 277
Black-body radiation 2 138—144
Black-body radiation, density of states for 215
Black-body radiation, entropy of 282 287
Black-body radiation, equilibrium in 139
Black-body radiation, low-temperature limit 215
Black-body radiation, Planck distribution for 144 216
Black-body radiation, quantum theory of 215f
Black-body radiation, Rayleigh — Jeans law 144 216
Black-body radiation, total energy of 142
Black-body radiation, ultraviolet catastrophe 144
Black-body radiation, wavenumber and 142—143
Bloch, Felix vf
Block diagonal 179 182—183
Bohr magneton 152 218
Bohr radius 152
Boltzmann distribution 88
Boltzmann, Ludwig 1
Boltzmann’s constant 60 188
Bose gas 246f 292
Bose particles 226
Bose — Einstein condensation 246
Bose — Einstein statistics 206 243f 292
Bosons 206 226—228 243
boundary conditions 161
Boundary conditions, fixed endpoints 117—120 126—134
Boundary conditions, periodic 126—132 140
Boundary conditions, Schrodinger equation and 160 (see also “Specific systems types”)
Boyle’s law 1
Brillouin zone 135 137
Brownian motion 42
Canonical distribution 50—54 184—186 276
canonical ensemble 55 87 187
Canonical ensemble, grand 229—233 290
Canonical ensemble, in magnetic field 148
Canonical ensemble, partition function for 56 229f
Canonical ensemble, phase space in 62
Canonical ensemble, Poisson brackets 38 252—257
Canonical ensemble, probability density and 79
Canonical ensemble, thermal randomness and 156
Canonical ensemble, volume element 26 258—261
Canonical transformation 9 38f 97 251—257
Center of mass 96f
chemical potential 232 238 291
Classical mechanics 3—23
Classical mechanics, applications of 74—156
Classical mechanics, central failure of 199
Classical mechanics, partition function in 196 224
Classical mechanics, quantum theory and 157 223
Clausius, Rudolf 1
Coarse-grain description 70
Coarse-grain description, ergodicity and 49 181
Coarse-grain description, phase space in 225
Commutators 164—165 289
Completeness relation 177 284
Compressibility 291
Conduction 238
Configuration-space integrals 75f 87f
Continuity, equation of 36
Correlation, statistical 31
Coulomb interactions 150 167
Coupling 65f 185f
Crystal 106f 284
Crystal, equilibrium in 134
Crystal, lattice structure 133—135 138
Crystal, oscillations in 110
Curie law 154
DeBroglie wavelength 237 240
Debye theory 210—214 224
Degeneracy 166f 178 181 226
Degrees of freedom 3 80
Degrees of freedom, degeneracy in 178
Degrees of freedom, energy and 94
Degrees of freedom, freezing out of 105—106
Degrees of freedom, in macroscopic systems 46 178
Degrees of freedom, observables and 165
Degrees of freedom, rotational 106
Degrees of freedom, vibrational 105—106
Delta function 16 110 174
Density matrix 162—163 171—176 182—184
Diagonal condition 172—173
Diagonalization 115
Diamagnetism 150 155 221
Diatomic molecules, classical statistical mechanics of 95—106
Diatomic molecules, diatomic gas 97 106 277 280
Diatomic molecules, partition function for 201f
Diatomic molecules, quantum statistical mechanics of 200—209
Diatomic molecules, rotational motion of 203f 285f
Diatomic molecules, specific heat of 104—106 224—225
Diatomic molecules, total energy of 280
Differential probability 24 29 31
Dipole moment 145—148
dispersion relation 137 215
Dispersion relation, Debye approximation 209—210
Dispersion relation, linear chain and 123
Dissociation 101 106
Distribution function, canonical ensemble and 79f
Distribution function, constancy of 43—49 181—184
Distribution function, defined 25
Distribution function, dynamical variables in 33
Distribution function, expansion coefficients and 182
Distribution function, in parameter space 168
Distribution function, phase orbit and 35 171
Distribution function, probability density and 24—28 39
Distribution function, quantum form 170
Distribution function, time development of 39 171
Distribution function, wavefunction and 173
Drift velocity vector 36
Dulong — Petit law 109 138 192 214
Dynamical operators 159—173
Dynamical variables 3 24 33
Eddy currents 150
Ehrenfest’s theorem 42 171 174
Eigenfunctions 160f 165
Eigenvalues 195
Eigenvalues, defined 111 160
Eigenvalues, degenerate 281
Eigenvalues, normal mode frequencies and 120
Eigenvalues, number of 121
Eigenvalues, of operators 165f
Einstein — Bose theory 206 243f 292
Elastic continuum 132
electric field 139f
Electromagnetic fields 139 142 215
Electrons 226
Electrons, angular momentum of 151
Electrons, charge on 150
Electrons, gyromagnetic ratio 151
Electrons, kinetic energy for 150
Electrons, magnetic moment for 151 218
Energy 77
Energy, conservation of 11
Energy, degrees of freedom and 94 (see also “Hamilton’s equations” “Thermodynamic(s)” “Specific systems”)
Energy, energy surfaces 46—48 63f 73 179—181
| Energy, entropy and 62
Energy, hamiltonian and 3 93
Energy, mean square deviation of 67
Energy, partition function and 56
Ensemble average see “Mean values”
Entropy, as extensive quantity 68
Entropy, black-body radiation and 282 287
Entropy, Boltzmann’s constant 68
entropy, defined 61
Entropy, energy and 62
Entropy, expression for 60
Entropy, for coupled subsystems 67
Entropy, Hamilton’s equations and 72
Entropy, ideal gas and 69 78 284
Entropy, increase with time 72
Entropy, irreversibility and 69
Entropy, of Fermi gas 291
Entropy, paramagnetic 283
Entropy, partition function and 61 66
Entropy, phase extension and 68ff
Entropy, reversible path 69
Entropy, second law and 58
Entropy, statistical theory and 68 70
Equilibrium see “Thermal equilibrium”
Equipartition theorem 196
Equipartition theorem, diatomic molecules and 104 280
Equipartition theorem, harmonic oscillators and 199 (see also “Partition function”)
Equipartition theorem, total energy and 109 137 143
Equipartition theorem, virial theorem and 92—95
Ergodic systems 46—48 183—184
Error, experimental 49
Euler — Lagrange equations 8
Euler — Maclaurin formula 286
Euler’s theorem 93—94
expectation value 159
Exponential damping 81
Exponential(s) 64
Extensive quantities 67—70 291
Fermi energy 239 241
Fermi gases 238
Fermi gases, degenerate 240 242
Fermi gases, entropy in 291f
Fermi gases, thermal excitation of 240 241
Fermi momentum 239
Fermi statistics 206 226 233—242 244 291
fermions 206 226—227 234
ferromagnetism 222ff
Fine-grain descriptions 49 70f 180
Finite difference methods 127
First Brillouin zone 137
Fixed endpoints 117—120 123
Fluid mechanics 35f
Fourier series 265—266
Fourier transforms 158
Free energy 61 78
Free energy, in magnetic field 148 156
Free energy, partition function and 62 149
Freezing out 210
Freezing out, at low temperatures 199
Freezing out, of atomic parameters 152
Freezing out, of degrees of freedom 105f
Freezing out, of high energy modes 142
Freezing out, of oscillations 109
Freezing out, of rotational motion 205
Freezing out, of translational motion 197
Freezing out, of vibrational modes 209
Frictional force 11 72
Frictional force, diatomic 97 106 277 280
Frictional force, entropy in 69
Frictional force, equation of state for 79
Frictional force, expansion of 73
Frictional force, Gases 60 95 263
Frictional force, hamiltonian for 74 97
Frictional force, ideal gas law 85 104
Frictional force, isothermal compression of 280 (see also “Specific types parameters”)
Frictional force, kinetic theory of 33 82 263—264
Frictional force, monatomic 74 84 193—196 224
Frictional force, of bosons 244
Frictional force, of fermions 238
Frictional force, partition function for 76—77 104
Frictional force, pressure of 78
Frictional force, virial theorem for 82—85 89
Frictional force, work by 12f
Gauge theory 148—150
Gaussian dependence 29
Gaussian distributions 158
Gauss’s theorem 36
Generalized coordinates 3 80
Gibbs free energy 61n
Gibbs, J.W. v 1f 55 63 71 230
grand canonical ensemble 229—233 290f
Grand partition function 231
Gravitational force 277
Groundstate 189f
gyromagnetic ratio 217ff
Hamilton, W.R. 2
Hamiltonian function 43
Hamiltonian function, anharmonic terms 281 (see also “Specific applications systems”)
Hamiltonian function, as operator 160 183
Hamiltonian function, center-of-mass and 96
Hamiltonian function, defined 3
Hamiltonian function, diagonalized 115
Hamiltonian function, for monatomic gas 74
Hamiltonian function, magnetic fields and 148 216
Hamiltonian function, Maxwell equations and 141
Hamiltonian function, mean value of 93
Hamiltonian function, minimal substitution in 148
Hamiltonian function, partition function 67
Hamiltonian function, phase density and 44 50
Hamiltonian function, quadratic form 94
Hamiltonian function, total differential for 13
Hamiltonian function, virial theorem and 83—85
Hamilton’s equations 3—13 71 251 274
Hamilton’s equations, canonical transformations of 9
Hamilton’s equations, defined 3
Hamilton’s equations, dissipative processes 11
Hamilton’s equations, entropy and 72
Hamilton’s equations, first law and 55
Hamilton’s equations, forward integration of 15
Hamilton’s equations, geometrical interpretation of 14
Hamilton’s equations, invariance of 7
Hamilton’s equations, Liouville’s theorem and 36—38
Hamilton’s equations, Poisson bracket and 37
Hamilton’s equations, time-dependence and 115n (see also “Hamiltonian function” “Specific parameters”)
Harmonic oscillators 21f 125—129 281
Harmonic oscillators, canonical transformation and 131
Harmonic oscillators, energy surface for 46 47
Harmonic oscillators, mean energy of 197—199
Harmonic oscillators, normal coordinates for 110
Harmonic oscillators, spectrum of 196f
Harmonic oscillators, two-dimensional 275
Harmonic oscillators, uncoupled 115 141
heat capacity 77f 106 196
Heat capacity, Bose gas and 247
Heat capacity, constant-volume 104 189 191
Heat capacity, Fermi gas and 242
Heat capacity, molar 104 138
Heat, mechanical energy and 11f
Heisenberg principle 157 159
Helium 226 237 244
Helmholtz free energy 61n
Hermitian operators 161—164 175
Hydrogen, specific heat of 207f 284
Hydrogen, spectrum of 166f
Hydrogen, wavefunction for 207
Identical particles 225—229 237 284
information 69
Interaction potentials 85 88f
Interatomic potential 96f 102 117 200
Internal variables 12 94f
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