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Walecka J.D. Fundamentals of statistical mechanics
Walecka J.D.  Fundamentals of statistical mechanics









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: Fundamentals of statistical mechanics

: Walecka J.D.

:

Imperial College Press) The manuscript and lecture notes of Nobel physics laureate Felix Bloch, prepared posthumously. Lays the fundamentals for statistical mechanics, and features three sets of Bloch's handwritten lecture notes, plus all of his problem sets, dating back to 1933. For advanced undergraduates or graduate students


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: 27.07.2005

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Absolute temperature      58
Absolute zero      189
Additive property      3032 262
angular momentum      166 202 217
Antisymmetry      206 226 228
Atoms, Bohr radius      152
Atoms, crystal structures      106107
Atoms, dipolar interaction      282 (see also Specific particles parameters structures)
Atoms, distances in      212
Atoms, equilibrium position      107
Atoms, interatomic potential      96 116 118119
Atoms, magnetic moment of      151f
Atoms, orientation of      153
Avogadros number      v 60 279
Basis of solutions      127 160
Bernoulli, Daniel      1
Binding energy      101 118
Binomial theorem      277
Black-body radiation      2 138144
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      142143
Bloch, Felix      vf
Block diagonal      179 182183
Bohr magneton      152 218
Bohr radius      152
Boltzmann distribution      88
Boltzmann, Ludwig      1
Boltzmanns constant      60 188
Bose gas      246f 292
Bose particles      226
Bose Einstein condensation      246
Bose Einstein statistics      206 243f 292
Bosons      206 226228 243
boundary conditions      161
Boundary conditions, fixed endpoints      117120 126134
Boundary conditions, periodic      126132 140
Boundary conditions, Schrodinger equation and      160 (see also Specific systems types)
Boyles law      1
Brillouin zone      135 137
Brownian motion      42
Canonical distribution      5054 184186 276
canonical ensemble      55 87 187
Canonical ensemble, grand      229233 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 252257
Canonical ensemble, probability density and      79
Canonical ensemble, thermal randomness and      156
Canonical ensemble, volume element      26 258261
Canonical transformation      9 38f 97 251257
Center of mass      96f
chemical potential      232 238 291
Classical mechanics      323
Classical mechanics, applications of      74156
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      164165 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      133135 138
Crystal, oscillations in      110
Curie law      154
DeBroglie wavelength      237 240
Debye theory      210214 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      105106
Degrees of freedom, in macroscopic systems      46 178
Degrees of freedom, observables and      165
Degrees of freedom, rotational      106
Degrees of freedom, vibrational      105106
Delta function      16 110 174
Density matrix      162163 171176 182184
Diagonal condition      172173
Diagonalization      115
Diamagnetism      150 155 221
Diatomic molecules, classical statistical mechanics of      95106
Diatomic molecules, diatomic gas      97 106 277 280
Diatomic molecules, partition function for      201f
Diatomic molecules, quantum statistical mechanics of      200209
Diatomic molecules, rotational motion of      203f 285f
Diatomic molecules, specific heat of      104106 224225
Diatomic molecules, total energy of      280
Differential probability      24 29 31
Dipole moment      145148
dispersion relation      137 215
Dispersion relation, Debye approximation      209210
Dispersion relation, linear chain and      123
Dissociation      101 106
Distribution function, canonical ensemble and      79f
Distribution function, constancy of      4349 181184
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      2428 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      159173
Dynamical variables      3 24 33
Eddy currents      150
Ehrenfests 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 Hamiltons equations Thermodynamic(s) Specific systems)
Energy, energy surfaces      4648 63f 73 179181
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, Boltzmanns constant      68
entropy, defined      61
Entropy, energy and      62
Entropy, expression for      60
Entropy, for coupled subsystems      67
Entropy, Hamiltons 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      9295
Ergodic systems      4648 183184
Error, experimental      49
Euler Lagrange equations      8
Euler Maclaurin formula      286
Eulers theorem      9394
expectation value      159
Exponential damping      81
Exponential(s)      64
Extensive quantities      6770 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 233242 244 291
fermions      206 226227 234
ferromagnetism      222ff
Fine-grain descriptions      49 70f 180
Finite difference methods      127
First Brillouin zone      137
Fixed endpoints      117120 123
Fluid mechanics      35f
Fourier series      265266
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 263264
Frictional force, monatomic      74 84 193196 224
Frictional force, of bosons      244
Frictional force, of fermions      238
Frictional force, partition function for      7677 104
Frictional force, pressure of      78
Frictional force, virial theorem for      8285 89
Frictional force, work by      12f
Gauge theory      148150
Gaussian dependence      29
Gaussian distributions      158
Gausss theorem      36
Generalized coordinates      3 80
Gibbs free energy      61n
Gibbs, J.W.      v 1f 55 63 71 230
grand canonical ensemble      229233 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      8385
Hamiltons equations      313 71 251 274
Hamiltons equations, canonical transformations of      9
Hamiltons equations, defined      3
Hamiltons equations, dissipative processes      11
Hamiltons equations, entropy and      72
Hamiltons equations, first law and      55
Hamiltons equations, forward integration of      15
Hamiltons equations, geometrical interpretation of      14
Hamiltons equations, invariance of      7
Hamiltons equations, Liouvilles theorem and      3638
Hamiltons equations, Poisson bracket and      37
Hamiltons equations, time-dependence and      115n (see also Hamiltonian function Specific parameters)
Harmonic oscillators      21f 125129 281
Harmonic oscillators, canonical transformation and      131
Harmonic oscillators, energy surface for      46 47
Harmonic oscillators, mean energy of      197199
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      161164 175
Hydrogen, specific heat of      207f 284
Hydrogen, spectrum of      166f
Hydrogen, wavefunction for      207
Identical particles      225229 237 284
information      69
Interaction potentials      85 88f
Interatomic potential      96f 102 117 200
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