| Preface |
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1 | (5) |
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The Nature of the Problem |
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1 | (2) |
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3 | (3) |
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6 | (12) |
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Definitions and Nomenclature |
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6 | (1) |
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7 | (1) |
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8 | (1) |
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9 | (1) |
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9 | (1) |
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Example Groups of Finite Order |
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10 | (2) |
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Conjugate Elements and Class Structure |
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12 | (1) |
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Normal Divisors and Factor Groups |
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13 | (2) |
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15 | (3) |
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16 | (1) |
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17 | (1) |
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Theory of Group Representations |
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18 | (32) |
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18 | (2) |
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Proof of the Orthogonality Theorem |
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20 | (5) |
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The Character of a Representation |
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25 | (3) |
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Construction of Character Tables |
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28 | (1) |
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Decomposition of Reducible Representations |
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29 | (2) |
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Application of Representation Theory in Quantum Mechanics |
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31 | (6) |
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Illustrative Representations of Abelian Groups |
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37 | (2) |
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Basis Functions for Irreducible Representations |
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39 | (4) |
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43 | (3) |
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Direct-product Representations within a Group |
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46 | (4) |
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47 | (1) |
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48 | (2) |
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Physical Applications of Group Theory |
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50 | (44) |
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Crystal-symmetry Operators |
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51 | (3) |
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The Crystallographic Point Groups |
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54 | (8) |
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Irreducible Representations of the Point Groups |
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62 | (3) |
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Elementary Representations of the Three-dimensional Rotation Group |
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65 | (2) |
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Crystal-field Splitting of Atomic Energy Levels |
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67 | (2) |
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Intermediate Crystal-field-splitting Case |
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69 | (6) |
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Weak-crystal-field Case and Crystal Double Groups |
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75 | (3) |
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Introduction of Spin Effects in the Medium-field Case |
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78 | (2) |
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Group-theoretical Matrix-element Theorems |
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80 | (2) |
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Selection Rules and Parity |
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82 | (5) |
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87 | (2) |
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Application of Group Theory to Directed Valence |
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89 | (5) |
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92 | (1) |
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93 | (1) |
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Full Rotation Group and Angular Momentum |
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94 | (60) |
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Rotational Transformation Properties and Angular Momentum |
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94 | (4) |
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98 | (3) |
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Representation of Rotations through Eulerian Angles |
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101 | (2) |
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Homomorphism with the Unitary Group |
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103 | (3) |
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Representations of the Unitary Group |
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106 | (3) |
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Representation of the Rotation Group by Representations of the Unitary Group |
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109 | (2) |
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Application of the Rotation-representation Matrices |
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111 | (4) |
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Vector Model for Addition of Angular Momenta |
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115 | (2) |
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The Wigner or Clebsch-Gordan Coefficients |
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117 | (4) |
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Notation, Tabulations, and Symmetry Properties of the Wigner Coefficients |
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121 | (3) |
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124 | (7) |
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The Wigner-Eckart Theorem |
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131 | (2) |
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133 | (4) |
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Application of Racah Coefficients |
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137 | (2) |
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The Rotation-Inversion Group |
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139 | (2) |
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141 | (6) |
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147 | (7) |
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151 | (2) |
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153 | (1) |
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Quantum Mechanics of Atoms |
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154 | (56) |
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Review of Elementary Atomic Structure and Nomenclature |
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155 | (2) |
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157 | (1) |
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Approximate Eigenfunctions |
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157 | (5) |
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Calculation of Matrix Elements between Determinantal Wavefunctions |
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162 | (5) |
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167 | (3) |
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Calculation of L-S-term Energies |
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170 | (3) |
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Evaluation of Matrix Elements of the Energy |
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173 | (5) |
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Eigenfunctions and Angular-momentum Operations |
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178 | (3) |
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Calculation of Fine Structure |
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181 | (7) |
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188 | (5) |
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Magnetic Hyperfine Structure |
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193 | (8) |
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Electric Hyperfine Structure |
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201 | (9) |
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206 | (2) |
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208 | (2) |
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Molecular Quantum Mechanics |
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210 | (57) |
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Born-Oppenheimer Approximation |
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210 | (3) |
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Simple Electronic Eigenfunctions |
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213 | (3) |
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Irreducible Representations for Linear Molecules |
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216 | (3) |
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219 | (1) |
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220 | (3) |
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223 | (3) |
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Orthogonal Atomic Orbitals |
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226 | (1) |
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Group Theory and Molecular Orbitals |
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227 | (6) |
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Selection Rules for Electronic Transitions |
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233 | (1) |
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Vibration of Diatomic Molecules |
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234 | (4) |
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Normal Modes in Polyatomic Molecules |
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238 | (4) |
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Group Theory and Normal Modes |
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242 | (6) |
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Selection Rules for Vibrational Transitions |
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248 | (2) |
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250 | (2) |
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Effect of Nuclear Statistics on Molecular Rotation |
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252 | (3) |
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255 | (2) |
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Vibration-Rotation Interaction |
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257 | (3) |
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Rotation-Electronic Coupling |
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260 | (7) |
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264 | (2) |
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266 | (1) |
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267 | (68) |
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Symmetry Properties in Solids |
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267 | (3) |
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The Reciprocal Lattice and Brillouin Zones |
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270 | (5) |
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Form of Energy-band Wavefunctions |
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275 | (4) |
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Crystal Symmetry and the Group of the k Vector |
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279 | (2) |
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Pictorial Consideration of Eigenfunctions |
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281 | (3) |
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Formal Consideration of Degeneracy and Compatibility |
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284 | (6) |
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Group Theory and the Plane-wave Approximation |
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290 | (3) |
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Connection between Tight- and Loose-binding Approximations |
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293 | (2) |
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Spin-orbit Coupling in Band Theory |
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295 | (2) |
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Time Reversal in Band Theory |
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297 | (2) |
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299 | (4) |
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Symmetries of Magnetic Structures |
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303 | (6) |
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The Landau Theory of Second-order Phase Transitions |
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309 | (2) |
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Irreducible Representations of Magnetic Groups |
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311 | (6) |
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313 | (2) |
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315 | (2) |
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A Review of Vectors, Vector Spaces, and Matrices |
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317 | (6) |
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B Character Tables for Point-symmetry Groups |
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323 | (8) |
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C Tables of ck and ak Coefficients for s, p, and d Electrons |
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331 | (4) |
| Index |
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335 | |
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