| Preface |
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xii | |
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Electrons in one-dimensional periodic potentials |
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1 | (36) |
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The Bloch theorem for one-dimensional periodicity |
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2 | (3) |
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Energy levels in a periodic array of quantum wells |
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5 | (3) |
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Electron tunneling and energy bands |
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8 | (8) |
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Transmission and reflection of electrons through an arbitrary potential |
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8 | (6) |
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Electron tunneling through a periodic potential |
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14 | (2) |
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The tight-binding approximation |
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16 | (8) |
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Expansion in localized orbitals |
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16 | (2) |
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Tridiagonal matrices and continued fractions |
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18 | (6) |
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Plane waves and nearly free-electron approximation |
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24 | (5) |
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24 | (3) |
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The Mathieu potential and the continued fraction solution |
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27 | (2) |
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Some dynamical aspects of electrons in band theory |
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29 | (8) |
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35 | (2) |
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Geometrical description of crystals: direct and reciprocal lattices |
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37 | (40) |
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Simple lattices and composite lattices |
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38 | (5) |
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Periodicity and Bravais lattices |
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38 | (3) |
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Simple and composite crystal structures |
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41 | (2) |
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Geometrical description of some crystal structures |
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43 | (10) |
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Wigner-Seitz primitive cells |
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53 | (1) |
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54 | (5) |
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Definitions and basic properties |
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54 | (2) |
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Planes and directions in Bravais lattices |
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56 | (3) |
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59 | (3) |
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Translational symmetry and quantum mechanical aspects |
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62 | (8) |
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Translational symmetry and Bloch wavefunctions |
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62 | (1) |
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The parametric k . p Hamiltonian |
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63 | (4) |
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Cyclic boundary conditions |
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67 | (1) |
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Special k points for averaging over the Brillouin zone |
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68 | (2) |
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Density-of-states and critical points |
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70 | (7) |
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75 | (2) |
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The Sommerfeld free-electron theory of metals |
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77 | (25) |
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Quantum theory of the free-electron gas |
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77 | (5) |
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Fermi-Dirac distribution function and chemical potential |
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82 | (4) |
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Electronic specific heat in metals and thermodynamic functions |
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86 | (2) |
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Thermionic emission from metals |
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88 | (14) |
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Appendix A. Outline of statistical physics and thermodynamic relations |
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89 | (1) |
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Microcanonical ensemble and thermodynamic quantities |
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89 | (2) |
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Canonical ensemble and thermodynamic quantities |
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91 | (2) |
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Grand canonical ensemble and thermodynamic quantities |
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93 | (2) |
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Appendix B. Fermi-Dirac and Bose-Einstein statistics for independent particles |
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95 | (3) |
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Appendix C. Modified Fermi-Dirac statistics in a model of correlation effects |
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98 | (2) |
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100 | (2) |
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The one-electron approximation and beyond |
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102 | (41) |
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Introductory remarks on the many-electron problem |
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103 | (1) |
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104 | (2) |
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Identical particles and determinantal wavefunctions |
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106 | (1) |
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Matrix elements between determinantal states |
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107 | (3) |
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The Hartree-Fock equations |
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110 | (11) |
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Variational approach and Hartree-Fock equations |
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110 | (3) |
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Ground-state energy, ionization energies and transition energies |
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113 | (3) |
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Hartree-Fock equations and transition energies in closed-shell systems |
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116 | (3) |
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Hartree-Fock-Slater and Hartree-Fock-Roothaan approximations |
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119 | (2) |
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Overview of approaches beyond the one-electron approximation |
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121 | (1) |
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Electronic properties and phase diagram of the homogeneous electron gas |
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122 | (8) |
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The density functional theory and the Kohn-Sham equations |
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130 | (13) |
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Appendix A. Bielectronic integrals among spin-orbitals |
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137 | (1) |
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Appendix B. Outline of second quantization formalism for identical fermions |
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138 | (3) |
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Appendix C. An integral on the Fermi sphere |
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141 | (1) |
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142 | (1) |
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143 | (56) |
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Basic assumptions of the band theory |
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143 | (2) |
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The tight-binding method (LCAO method) |
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145 | (9) |
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Description of the method for simple lattices |
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145 | (3) |
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Description of the tight-binding method for composite lattices |
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148 | (2) |
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Illustrative applications of the tight-binding scheme |
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150 | (4) |
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The orthogonalized plane wave (OPW) method |
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154 | (9) |
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The pseudopotential method |
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163 | (6) |
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169 | (2) |
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The augmented plane wave (APW) method |
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171 | (6) |
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Description of the method |
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171 | (3) |
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Expression and evaluation of the matrix elements of the APW method |
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174 | (3) |
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The Green's function method (KKR method) |
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177 | (7) |
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Scattering integral equation for a generic potential |
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178 | (2) |
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Scattering integral equation for a periodic muffin-tin potential |
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180 | (3) |
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Expression and evaluation of the structure coefficients |
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183 | (1) |
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Other methods and developments in electronic structure calculations |
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184 | (15) |
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The linearized cellular methods |
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184 | (1) |
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The Lanczos or recursion method |
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185 | (5) |
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Modified Lanczos method for excited states |
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190 | (1) |
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Renormalization method for electronic systems |
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191 | (5) |
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196 | (3) |
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Electronic properties of selected crystals |
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199 | (31) |
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Band structure and cohesive energy of rare-gas solids |
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200 | (7) |
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General features of band structure of rare-gas solids |
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200 | (3) |
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Cohesive energy of rare-gas solids |
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203 | (4) |
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Electronic properties of ionic crystals |
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207 | (11) |
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Introductory remarks and Madelung constant |
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207 | (7) |
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Considerations on bands and bonds in ionic crystals |
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214 | (4) |
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Covalent crystals with diamond structure |
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218 | (4) |
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Band structures and Fermi surfaces of some metals |
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222 | (8) |
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228 | (2) |
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Excitons, plasmons and dielectric screening in crystals |
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230 | (38) |
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Exciton states in crystals |
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231 | (8) |
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Plasmon excitations in crystals |
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239 | (1) |
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General considerations on the longitudinal dielectric function |
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240 | (2) |
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Static dielectric screening in metals with the Thomas-Fermi model |
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242 | (3) |
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Static dielectric screening in metals with the Lindhard model |
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245 | (5) |
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Dynamic dielectric screening in metals and plasmon modes |
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250 | (4) |
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Quantum expression of the longitudinal dielectric function in materials |
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254 | (5) |
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Quantum expression of the longitudinal dielectric function in crystals |
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259 | (3) |
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Longitudinal dielectric function and energy-loss of a fast charged particle |
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262 | (6) |
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Appendix A. Lindhard dielectric function for the free-electron gas |
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263 | (3) |
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266 | (2) |
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Interacting electronic-nuclear systems and the adiabatic principle |
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268 | (39) |
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Electronic-nuclear systems and adiabatic potential-energy surfaces |
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269 | (3) |
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Non-degenerate adiabatic surface and nuclear dynamics |
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272 | (6) |
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Non-degenerate adiabatic surface and classical nuclear dynamics |
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272 | (1) |
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Non-degenerate adiabatic surface and quantum nuclear dynamics |
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273 | (5) |
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Degenerate adiabatic surfaces and Jahn-Teller systems |
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278 | (16) |
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Degenerate adiabatic surfaces and nuclear dynamics |
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278 | (4) |
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The Jahn-Teller effect for doubly degenerate electronic states |
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282 | (7) |
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The Jahn-Teller effect for triply degenerate electronic states |
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289 | (5) |
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The Hellmann-Feynman theorem and electronic-nuclear systems |
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294 | (3) |
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General considerations on the Hellmann-Feynman theorem |
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294 | (2) |
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Charge density and atomic forces |
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296 | (1) |
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Parametric Hamiltonians and Berry phase |
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297 | (4) |
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Macroscopic electric polarization in crystals and Berry phase |
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301 | (6) |
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305 | (2) |
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Lattice dynamics of crystals |
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307 | (42) |
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Dynamics of monatomic one-dimensional lattices |
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308 | (4) |
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Dynamics of diatomic one-dimensional lattices |
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312 | (3) |
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Dynamics of general three-dimensional crystals |
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315 | (8) |
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Quantum theory of the harmonic crystal |
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323 | (2) |
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Lattice heat capacity. Einstein and Debye models |
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325 | (2) |
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Considerations on anharmonic effects and melting of solids |
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327 | (2) |
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Optical phonons and polaritons in polar crystals |
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329 | (20) |
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329 | (2) |
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Lattice vibrations in polar crystals and polaritons |
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331 | (7) |
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Local field effects on polaritons |
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338 | (6) |
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Appendix A. Quantum theory of the linear harmonic oscillator |
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344 | (4) |
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348 | (1) |
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Scattering of particles by crystals |
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349 | (40) |
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349 | (3) |
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Elastic scattering of X-rays from crystals |
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352 | (11) |
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Elastic scattering of X-rays and Bragg diffraction condition |
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352 | (6) |
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Elastic scattering of X-rays and intensity of diffracted beams |
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358 | (5) |
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Inelastic scattering of particles and phonon spectra of crystals |
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363 | (5) |
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Compton scattering and electron momentum density |
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368 | (5) |
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Diffusion of particles by a single elastically-bound scatterer |
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373 | (7) |
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Dynamical structure factor of a single scattering center |
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373 | (4) |
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Dynamical structure factor of a three-dimensional harmonic oscillator |
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377 | (3) |
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Diffusion of particles by a crystal and effects of lattice vibrations |
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380 | (4) |
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384 | (5) |
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387 | (2) |
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Optical and transport properties in metals |
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389 | (36) |
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Macroscopic theory of optical constants in homogeneous materials |
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390 | (5) |
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The Drude theory of the optical properties of free carriers |
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395 | (8) |
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Transport properties and Boltzmann equation |
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403 | (3) |
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Static and dynamic conductivity in metals |
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406 | (7) |
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Static conductivity with the Boltzmann equation |
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406 | (1) |
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Frequency and wavevector dependence of the conductivity |
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407 | (3) |
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410 | (3) |
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Boltzmann treatment and quantum treatment of intraband transitions |
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413 | (1) |
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The Boltzmann equation in electric fields and temperature gradients |
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414 | (11) |
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The transport equations in general form |
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414 | (4) |
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418 | (6) |
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424 | (1) |
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Optical properties of semiconductors and insulators |
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425 | (48) |
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Quantum expression of the transverse dielectric function in materials |
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426 | (7) |
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Optical constants of homogeneous media in the linear response theory |
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426 | (5) |
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Optical constants and Green's function of the electronic system |
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431 | (2) |
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Quantum theory of band-to-band optical transitions and critical points |
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433 | (5) |
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Indirect phonon-assisted transitions |
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438 | (5) |
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443 | (3) |
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Exciton effects on the optical properties |
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446 | (6) |
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Fano resonances and absorption lineshapes |
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452 | (6) |
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Optical properties of vibronic systems |
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458 | (15) |
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Optical properties of the Franck-Condon vibronic model |
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458 | (7) |
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Optical properties of typical Jahn-Teller systems |
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465 | (4) |
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Appendix A. Transitions rates at first and higher orders of perturbation theory |
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469 | (2) |
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471 | (2) |
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Transport in intrinsic and homogeneously doped semiconductors |
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473 | (33) |
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Fermi level and carrier density in intrinsic semiconductors |
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473 | (5) |
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Impurity levels in semiconductors |
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478 | (7) |
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Fermi level and carrier density in doped semiconductors |
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485 | (5) |
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Thermionic emission in semiconductors |
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490 | (1) |
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Non-equilibrium carrier distributions |
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491 | (7) |
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Drift and diffusion currents |
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491 | (6) |
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Generation and recombination of electron-hole pairs in semiconductors |
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497 | (1) |
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Solutions of typical transport equations in uniformly doped semiconductors |
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498 | (8) |
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504 | (2) |
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Transport in inhomogeneous semiconductors |
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506 | (37) |
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Properties of the pn junction at equilibrium |
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506 | (6) |
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Current-voltage characteristics of the pn junction |
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512 | (5) |
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The bipolar junction transistor |
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517 | (3) |
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The junction field-effect transistor (JFET) |
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520 | (4) |
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Semiconductor heterojunctions |
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524 | (3) |
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Metal-semiconductor contacts and MESFET transistor |
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527 | (6) |
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The metal-oxide-semiconductor structure and MOSFET transistor |
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533 | (10) |
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541 | (2) |
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Electron gas in magnetic fields |
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543 | (43) |
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Magnetization and magnetic susceptibility |
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544 | (2) |
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Energy levels and density-of-states of a free-electron gas in magnetic fields |
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546 | (8) |
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Energy levels of the two-dimensional electron gas in magnetic fields |
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547 | (4) |
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Energy levels of the three-dimensional electron gas in magnetic fields |
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551 | (3) |
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Orbital magnetic susceptibility and de Haas-van Alphen effect |
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554 | (8) |
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Orbital magnetic susceptibility of a two-dimensional electron gas |
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554 | (5) |
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Orbital magnetic susceptibility of a three-dimensional electron gas |
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559 | (3) |
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Spin paramagnetism of a free-electron gas |
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562 | (2) |
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Magnetoresistivity and classical Hall effect |
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564 | (5) |
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569 | (17) |
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Appendix A. Free energy of an electron gas in a uniform magnetic field |
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574 | (5) |
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Appendix B. Generalized orbital magnetic susceptibility of the free-electron gas |
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579 | (6) |
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585 | (1) |
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Magnetic properties of localized systems and Kondo impurities |
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586 | (33) |
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Quantum mechanical treatment of magnetic susceptibility |
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587 | (2) |
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Magnetic susceptibility of closed-shell systems |
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589 | (2) |
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Permanent magnetic dipoles in atoms or ions with partially filled shells |
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591 | (2) |
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Paramagnetism of localized magnetic moments |
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593 | (5) |
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Localized magnetic states in normal metals |
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598 | (4) |
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Dilute magnetic alloys and the resistance minimum phenomenon |
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602 | (10) |
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Some phenomenological aspects |
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602 | (2) |
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The resistance minimum phenomenon |
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604 | (4) |
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Microscopic origin of the Kondo interaction: a molecular model |
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608 | (4) |
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Magnetic impurity in normal metals at very low temperatures |
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612 | (7) |
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618 | (1) |
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Magnetic ordering in crystals |
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619 | (44) |
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Ferromagnetism and the Weiss molecular field |
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620 | (7) |
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Microscopic origin of the coupling between localized magnetic moments |
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627 | (8) |
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Antiferromagnetism in the mean field approximation |
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635 | (3) |
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Spin waves and magnons in ferromagnetic crystals |
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638 | (5) |
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The Ising model with the transfer matrix method |
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643 | (4) |
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The Ising model with the renormalization group theory |
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647 | (12) |
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The Stoner-Hubbard itinerant electron model for magnetism |
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659 | (4) |
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662 | (1) |
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663 | (59) |
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Some phenomenolgical aspects of superconductors |
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664 | (8) |
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672 | (6) |
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Ground state for a superconductor in the BCS theory at zero temperature |
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678 | (8) |
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Variational determination of the ground-state wavefunction |
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678 | (4) |
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Ground-state energy and isotopic effect |
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682 | (2) |
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Momentum distribution and coherence length |
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684 | (2) |
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Excited states of superconductors at zero temperature |
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686 | (7) |
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The Bogoliubov canonical transformation |
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686 | (5) |
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Persistent currents in superconductors |
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691 | (1) |
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Electron tunneling into superconductors |
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691 | (2) |
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Treatment of superconductors at finite temperature and heat capacity |
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693 | (5) |
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Diamagnetism of superconductors and Meissner effect |
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698 | (6) |
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The phenomenological London model |
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698 | (4) |
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Pippard electrodynamics and effective magnetic penetration depth |
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702 | (2) |
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Macroscopic quantum phenomena |
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704 | (7) |
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Order parameter in superconductors and Ginzburg-Landau theory |
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704 | (4) |
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Magnetic flux quantization |
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708 | (1) |
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Type-I and type-II superconductors |
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709 | (2) |
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Cooper pair tunneling between superconductors and Josephson effects |
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711 | (11) |
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Appendix A. The phonon-induced electron-electron interaction |
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717 | (3) |
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720 | (2) |
| Subject index |
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722 | |
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