Preface |
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xv | |
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1 | (85) |
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1.1 Where Do Bands Come From? Why Solid State Physics Requires a New Way of Thinking |
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1 | (9) |
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1.1.1 Energy Splitting Due to Wave Function Overlap |
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2 | (5) |
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1.1.2 The LCAO Approximation |
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7 | (2) |
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1.1.3 General Remarks on Bands |
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9 | (1) |
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1.2 The Kronig-Penney Model |
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10 | (6) |
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16 | (2) |
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1.4 Bravais Lattices and Reciprocal Space |
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18 | (9) |
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27 | (4) |
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1.6 General Properties of Bloch Functions |
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31 | (4) |
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1.7 Boundary Conditions in a Finite Crystal |
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35 | (3) |
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38 | (6) |
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1.8.1 Density of States at Critical Points |
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39 | (2) |
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1.8.2 Disorder and Density of States |
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41 | (3) |
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1.9 Electron Band Calculations in Three Dimensions |
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44 | (17) |
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1.9.1 How to Read a Band Diagram |
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44 | (3) |
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1.9.2 The Tight-Binding Approximation and Wannier Functions |
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47 | (5) |
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1.9.3 The Nearly Free Electron Approximation |
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52 | (3) |
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55 | (5) |
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1.9.5 Other Methods of Calculating Band Structure |
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60 | (1) |
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1.10 Angle-Resolved Photoemission Spectroscopy |
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61 | (4) |
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1.11 Why Are Bands Often Completely Full or Empty? Bands and Molecular Bonds |
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65 | (9) |
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65 | (3) |
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1.11.2 Classes of Electronic Structure |
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68 | (1) |
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69 | (3) |
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1.11.4 Dangling Bonds and Defect States |
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72 | (2) |
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74 | (5) |
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1.13 Spin in Electron Bands |
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79 | (7) |
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80 | (2) |
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1.13.2 Spin-Orbit Effects on the /r-Dependence of Bands |
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82 | (3) |
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85 | (1) |
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2 Electronic Quasiparticles |
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86 | (71) |
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86 | (2) |
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88 | (3) |
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91 | (4) |
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2.4 Metals and the Fermi Gas |
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95 | (6) |
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2.4.1 Isotropic Fermi Gas at T = 0 |
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97 | (2) |
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2.4.2 Fermi Gas at Finite Temperature |
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99 | (2) |
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2.5 Basic Behavior of Semiconductors |
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101 | (9) |
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2.5.1 Equilibrium Populations of Electrons and Holes |
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102 | (2) |
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2.5.2 Semiconductor Doping |
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104 | (2) |
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2.5.3 Equilibrium Populations in Doped Semiconductors |
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106 | (2) |
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2.5.4 The Mott Transition |
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108 | (2) |
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2.6 Band Bending at Interfaces |
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110 | (9) |
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2.6.1 Metal-to-Metal Interfaces |
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110 | (2) |
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2.6.2 Doped Semiconductor Junctions |
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112 | (3) |
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2.6.3 Metal-Semiconductor Junctions |
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115 | (3) |
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2.6.4 Junctions of Undoped Semiconductors |
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118 | (1) |
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119 | (9) |
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2.7.1 Bipolar Transistors |
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119 | (4) |
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2.7.2 Field Effect Transistors |
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123 | (5) |
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128 | (14) |
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2.8.1 Density of States in Quantum-Confined Systems |
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130 | (2) |
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2.8.2 Superlattices and Bloch Oscillations |
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132 | (5) |
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2.8.3 The Two-Dimensional Electron Gas |
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137 | (1) |
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2.8.4 One-Dimensional Electron Transport |
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137 | (2) |
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2.8.5 Quantum Dots and Coulomb Blockade |
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139 | (3) |
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2.9 Landau Levels and Quasiparticles in Magnetic Field |
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142 | (15) |
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2.9.1 Quantum Mechanical Calculation of Landau Levels |
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144 | (3) |
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2.9.2 De Haas-Van Alphen and Shubnikov-De Haas Oscillations |
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147 | (1) |
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2.9.3 The Integer Quantum Hall Effect |
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148 | (5) |
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2.9.4 The Fractional Quantum Hall Effect and Higher-Order Quasiparticles |
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153 | (3) |
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156 | (1) |
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3 Classical Waves in Anisotropic Media |
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157 | (55) |
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3.1 The Coupled Harmonic Oscillator Model |
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157 | (11) |
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3.1.1 Harmonic Approximation of the Interatomic Potential |
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158 | (1) |
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159 | (4) |
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3.1.3 Vibrational Modes in Higher Dimensions |
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163 | (5) |
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168 | (1) |
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3.3 Phase Velocity and Group Velocity in Anisotropic Media |
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169 | (2) |
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3.4 Acoustic Waves in Anisotropic Crystals |
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171 | (11) |
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3.4.1 Stress and Strain Definitions: Elastic Constants |
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172 | (6) |
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3.4.2 The Christoffel Wave Equation |
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178 | (2) |
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3.4.3 Acoustic Wave Focusing |
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180 | (2) |
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3.5 Electromagnetic Waves in Anisotropic Crystals |
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182 | (11) |
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3.5.1 Maxwell's Equations in an Anisotropic Crystal |
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182 | (3) |
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185 | (5) |
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3.5.3 The Index Ellipsoid |
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190 | (3) |
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193 | (3) |
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3.7 Piezoelectric Materials |
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196 | (4) |
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3.8 Reflection and Transmission at Interfaces |
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200 | (7) |
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3.8.1 Optical Fresnel Equations |
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200 | (3) |
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3.8.2 Acoustic Fresnel Equations |
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203 | (3) |
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3.8.3 Surface Acoustic Waves |
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206 | (1) |
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3.9 Photonic Crystals and Periodic Structures |
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207 | (5) |
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210 | (2) |
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212 | (51) |
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4.1 The Quantized Harmonic Oscillator |
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212 | (3) |
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215 | (5) |
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220 | (4) |
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224 | (5) |
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4.5 Spatial Field Operators |
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229 | (3) |
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4.6 Electron Fermi Field Operators |
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232 | (2) |
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4.7 First-Order Time-Dependent Perturbation Theory: Fermi's Golden Rule |
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234 | (5) |
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4.8 The Quantum Boltzmann Equation |
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239 | (11) |
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4.8.1 Equilibrium Distributions of Quantum Particles |
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244 | (3) |
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4.8.2 The H-Theorem and the Second Law |
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247 | (3) |
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4.9 Energy Density of Solids |
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250 | (8) |
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4.9.1 Density of States of Phonons and Photons |
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251 | (1) |
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4.9.2 Planck Energy Density |
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252 | (1) |
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4.9.3 Heat Capacity of Phonons |
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253 | (3) |
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4.9.4 Electron Heat Capacity: Sommerfeld Expansion |
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256 | (2) |
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4.10 Thermal Motion of Atoms |
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258 | (5) |
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262 | (1) |
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5 Interactions of Quasiparticles |
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263 | (64) |
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5.1 Electron-Phonon Interactions |
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264 | (9) |
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5.1.1 Deformation Potential Scattering |
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264 | (4) |
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5.1.2 Piezoelectric Scattering |
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268 | (2) |
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5.1.3 Frohlich Scattering |
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270 | (1) |
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5.1.4 Average Electron-Phonon Scattering Time |
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271 | (2) |
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5.2 Electron-Photon Interactions |
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273 | (7) |
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5.2.1 Optical Transitions Between Semiconductor Bands |
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274 | (3) |
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5.2.2 Multipole Expansion |
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277 | (3) |
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5.3 Interactions with Defects: Rayleigh Scattering |
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280 | (7) |
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5.4 Phonon-Phonon Interactions |
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287 | (7) |
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290 | (2) |
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5.4.2 Crystal Phase Transitions |
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292 | (2) |
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5.5 Electron-Electron Interactions |
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294 | (8) |
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5.5.1 Semiclassical Estimation of Screening Length |
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297 | (3) |
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5.5.2 Average Electron-Electron Scattering Time |
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300 | (2) |
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5.6 The Relaxation-Time Approximation and the Diffusion Equation |
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302 | (4) |
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306 | (2) |
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5.8 Electrical Conductivity |
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308 | (5) |
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5.9 Thermoelectricity: Drift and Diffusion of a Fermi Gas |
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313 | (5) |
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318 | (1) |
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5.11 The Boltzmann Transport Equation |
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319 | (3) |
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5.12 Drift of Defects and Dislocations: Plasticity |
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322 | (5) |
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325 | (2) |
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327 | (48) |
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6.1 Definition of a Group |
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327 | (2) |
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329 | (4) |
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333 | (3) |
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6.4 Equating Physical States with the Basis States of Representations |
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336 | (4) |
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6.5 Reducing Representations |
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340 | (6) |
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6.6 Multiplication Rules for Outer Products |
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346 | (5) |
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6.7 Review of Types of Operators |
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351 | (1) |
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6.8 Effects of Lowering Symmetry |
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352 | (3) |
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6.9 Spin and Time Reversal Symmetry |
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355 | (4) |
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6.10 Allowed and Forbidden Transitions |
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359 | (7) |
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6.10.1 Second-Order Transitions |
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361 | (1) |
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6.10.2 Quadrupole Transitions |
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362 | (4) |
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6.11 Perturbation Methods |
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366 | (9) |
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6.11.1 Group Theory in k p Theory |
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366 | (4) |
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6.11.2 Method of Invariants |
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370 | (4) |
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374 | (1) |
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7 The Complex Susceptibility |
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375 | (51) |
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7.1 A Microscopic View of the Dielectric Constant |
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375 | (8) |
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7.1.1 Fresnel Equations for the Complex Dielectric Function |
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380 | (2) |
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382 | (1) |
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7.2 Kramers-Kronig Relations |
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383 | (5) |
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7.3 Negative Index of Refraction: Metamaterials |
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388 | (3) |
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7.4 The Quantum Dipole Oscillator |
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391 | (8) |
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399 | (12) |
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399 | (3) |
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402 | (2) |
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7.5.3 Quantum Mechanical Formulation of Polaritons |
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404 | (7) |
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7.6 Nonlinear Optics and Photon-Photon Interactions |
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411 | (6) |
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7.6.1 Second-Harmonic Generation and Three-Wave Mixing |
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411 | (4) |
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7.6.2 Higher-Order Effects |
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415 | (2) |
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7.7 Acousto-Optics and Photon-Phonon Interactions |
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417 | (4) |
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421 | (5) |
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425 | (1) |
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8 Many-Body Perturbation Theory |
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426 | (80) |
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8.1 Higher-Order Time-Dependent Perturbation Theory |
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426 | (7) |
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433 | (2) |
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8.3 Shift of Bands with Temperature |
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435 | (1) |
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436 | (5) |
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8.5 Diagram Rules for Rayleigh-Schrodinger Perturbation Theory |
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441 | (5) |
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8.6 Feynman Perturbation Theory |
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446 | (8) |
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8.7 Diagram Rules for Feynman Perturbation Theory |
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454 | (3) |
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457 | (4) |
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8.9 Physical Meaning of the Green's Functions |
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461 | (6) |
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8.10 Finite Temperature Diagrams |
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467 | (4) |
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8.11 Screening and Plasmons |
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471 | (11) |
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475 | (4) |
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8.11.2 The Conductor-Insulator Transition and Screening |
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479 | (3) |
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8.12 Ground State Energy of the Fermi Sea: Density Functional Theory |
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482 | (4) |
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8.13 The Imaginary-Time Method for Finite Temperature |
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486 | (8) |
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8.14 Symmetrized Green's Functions |
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494 | (4) |
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8.15 Matsubara Calculations for the Electron Gas |
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498 | (8) |
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504 | (2) |
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9 Coherence and Correlation |
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506 | (58) |
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9.1 Density Matrix Formalism |
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507 | (3) |
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9.2 Magnetic Resonance: The Bloch Equations |
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510 | (10) |
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9.3 Optical Bloch Equations |
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520 | (3) |
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9.4 Quantum Coherent Effects |
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523 | (8) |
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9.5 Correlation Functions and Noise |
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531 | (5) |
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9.6 Correlations in Quantum Mechanics |
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536 | (4) |
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9.7 Particle-Particle Correlation |
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540 | (3) |
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9.8 The Fluctuation-Dissipation Theorem |
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543 | (5) |
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9.9 Current Fluctuations and the Nyquist Formula |
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548 | (2) |
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9.10 The Kubo Formula and Many-Body Theory of Conductivity |
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550 | (5) |
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555 | (9) |
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562 | (2) |
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10 Spin and Magnetic Systems |
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564 | (54) |
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10.1 Overview of Magnetic Properties |
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564 | (4) |
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10.2 Lande g-factor in Solids |
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568 | (2) |
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570 | (7) |
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10.3.1 Spontaneous Symmetry Breaking |
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571 | (4) |
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10.3.2 External Magnetic Field: Hysteresis |
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575 | (2) |
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10.4 Critical Exponents and Fluctuations |
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577 | (7) |
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10.5 Renormalization Group Methods |
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584 | (4) |
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10.6 Spin Waves and Goldstone Bosons |
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588 | (4) |
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10.7 Domains and Domain Walls |
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592 | (3) |
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10.8 Spin-Spin Interaction |
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595 | (17) |
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10.8.1 Ferromagnetic Instability |
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597 | (4) |
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10.8.2 Localized States and RKKY Exchange Interaction |
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601 | (6) |
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10.8.3 Electron-Hole Exchange |
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607 | (5) |
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10.9 Spin Flip and Spin Dephasing |
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612 | (6) |
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617 | (1) |
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11 Spontaneous Coherence in Matter |
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618 | (69) |
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11.1 Theory of the Ideal Bose Gas |
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620 | (3) |
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11.2 The Bogoliubov Model |
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623 | (3) |
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11.3 The Stability of the Condensate: Analogy with Ferromagnets |
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626 | (5) |
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11.4 Bose Liquid Hydrodynamics |
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631 | (3) |
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11.5 Superfluids versus Condensates |
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634 | (4) |
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11.6 Constructing Bosons from Fermions |
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638 | (3) |
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641 | (3) |
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644 | (4) |
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11.9 Excitation Spectrum of a Superconductor |
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648 | (10) |
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11.9.1 Density of States and Tunneling Spectroscopy |
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652 | (4) |
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11.9.2 Temperature Dependence of the Gap |
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656 | (2) |
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11.10 Magnetic Effects of Superconductors |
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658 | (11) |
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660 | (3) |
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11.10.2 Flux Quantization |
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663 | (2) |
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11.10.3 Type I and Type II Superconductors |
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665 | (4) |
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11.11 Josephson Junctions |
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669 | (5) |
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11.12 Spontaneous Optical Coherence: Lasing as a Phase Transition |
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674 | (3) |
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11.13 Excitonic Condensation |
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677 | (10) |
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11.13.1 Microcavity Polaritons |
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679 | (5) |
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11.13.2 Other Quasiparticle Condensates |
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684 | (1) |
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685 | (2) |
Appendix A Review of Bra-Ket Notation |
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687 | (2) |
Appendix B Review of Fourier Series and Fourier Transforms |
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689 | (3) |
Appendix C Delta-Function Identities |
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692 | (3) |
Appendix D Quantum Single Harmonic Oscillator |
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695 | (3) |
Appendix E Second-Order Perturbation Theory |
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698 | (6) |
Appendix F Relativistic Derivation of Spin Physics |
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704 | (6) |
Index |
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710 | |