Page 7 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics
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Contents vii
Chapter 8 Systems of identical particles 208
8.1 Permutations of identical particles 208
8.2 Bosons and fermions 217
8.3 Completeness relation 218
8.4 Non-interacting particles 220
8.5 The free-electron gas 226
8.6 Bose±Einstein condensation 229
Problems 230
Chapter 9 Approximation methods 232
9.1 Variation method 232
9.2 Linear variation functions 237
9.3 Non-degenerate perturbation theory 239
9.4 Perturbed harmonic oscillator 246
9.5 Degenerate perturbation theory 248
9.6 Ground state of the helium atom 256
Problems 260
Chapter 10 Molecular structure 263
10.1 Nuclear structure and motion 263
10.2 Nuclear motion in diatomic molecules 269
Problems 279
Appendix A Mathematical formulas 281
Appendix B Fourier series and Fourier integral 285
Appendix C Dirac delta function 292
Appendix D Hermite polynomials 296
Appendix E Legendre and associated Legendre polynomials 301
Appendix F Laguerre and associated Laguerre polynomials 310
Appendix G Series solutions of differential equations 318
Appendix H Recurrence relation for hydrogen-atom expectation values 329
Appendix I Matrices 331
Appendix J Evaluation of the two-electron interaction integral 341
Selected bibliography 344
Index 347
Physical constants
