Preface ........................................................ ix
Translators' foreword .......................................... xi
1 Atoms ........................................................ 1
1.1 Mean-field approximation and electronic configurations .. 1
1.2 Multiplets .............................................. 3
1.3 Coulomb and exchange integrals ......................... 10
1.4 Hartree's method ....................................... 13
References and further reading .............................. 14
2 Molecules ................................................... 16
2.1 The H2+ molecule ....................................... 16
2.2 The H2 molecule ........................................ 19
2.3 The configuration interaction .......................... 22
2.4 Second quantization .................................... 25
References and further reading .............................. 30
3 The Sommerfeld theory of metals ............................. 32
3.1 Classification of solids ............................... 32
3.2 The Sommerfeld theory .................................. 36
References and further reading .............................. 48
4 Band theory ................................................. 49
4.1 The periodic structure of crystals ..................... 49
4.2 Bloch's theorem ........................................ 52
4.3 An approach starting from the free electron picture .... 55
4.4 The Bloch orbital as a linear combination of atomic
orbitals ............................................... 59
4.5 Metals and insulators .................................. 61
4.6 The Wigner-Seitz theory ................................ 63
5 Magnetic impurities in metals ............................... 69
5.1 Local charge neutrality ................................ 69
5.2 The spherical representation ........................... 72
5.3 Charge distribution and the density of states .......... 78
5.4 Virtual bound states ................................... 80
5.5 The Anderson model I ................................... 84
5.6 The Anderson model II .................................. 90
5.7 The Coulomb interaction: UHF ........................... 97
5.8 Expansion in powers of U .............................. 104
5.9 s-d interaction ....................................... 106
5.10 Case with orbital degeneracy .......................... 115
References and further reading ............................. 119
6 The infrared divergence in metals .......................... 120
6.1 The Anderson orthogonality theorem .................... 120
6.2 Mahan's problem ....................................... 124
6.3 The thermal Green's function .......................... 127
6.4 Thermal Green's functions in the presence of local
potentials ............................................ 130
6.5 The partition function in the s-d problem ............. 132
6.6 The Nozieres-de Dominicis solution .................... 134
6.7 Calculation of the partition function ................. 136
6.8 A scaling approach .................................... 140
References and further reading ............................. 143
7 Wilson's theory ............................................ 144
7.1 Wilson's Hamiltonian .................................. 144
7.2 Perturbative expansions ............................... 150
7.3 Numerical calculations: scaling ....................... 154
7.4 Susceptibility and specific heat ...................... 159
References and further reading ............................. 164
8 Exact solution to the s-d problem .......................... 165
8.1 A one-dimensional model ............................... 165
8.2 The three-body problem ................................ 168
8.3 Symmetric groups ...................................... 175
8.4 The N-electron problem ................................ 176
8.5 Antisymmetrization .................................... 179
8.6 The eigenvalue problem ................................ 182
8.7 The integral equation ................................. 185
8.8 The ground state ...................................... 187
8.9 Susceptibility ........................................ 188
8.10 Universality .......................................... 192
8.11 The excited states .................................... 195
8.12 Free energy ........................................... 199
8.13 Specific heat ......................................... 204
References and further reading ............................. 208
9 Recent developments ........................................ 209
9.1 The spin-flip rate .................................... 209
9.2 The heavy electrons ................................... 211
9.3 Quantum dots .......................................... 214
References and further reading ............................. 217
Appendices .................................................... 218
A Matrix elements between Slater determinants ............. 218
В Spin function for TV"-electron systems .................. 221
С Fourier expansion of three-dimensional periodic
functions ............................................... 224
D Proof of eq. (5.29) ..................................... 225
E Relations between Green's functions ..................... 226
F Expansion of free energy to order J2 .................... 228
G Calculation of g± ....................................... 234
H Feynman's theorem ....................................... 236
I Elimination of adjacent pairs ........................... 237
J Proof of eq. (6.80) ..................................... 239
К Transformation from plane-wave representation to
spherical-wave representation ........................... 240
L Derivation of eq. (7.33) ................................ 241
M Derivation of eq. (7.35) ................................ 241
N Solution to the eigenvalue problem in §8.6 .............. 243
О Wiener-Hopf integral equation ........................... 253
P Analytic continuation of eq. (8.82) ..................... 255
Q Rewriting eqs. (8.115) and (8.116) ...................... 256
Index ......................................................... 259
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