SternGerlach experiment 196 Spin one systems 200 The classical limit 201 75

Sterngerlach experiment 196 spin one systems 200 the

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Stern–Gerlach experiment 196 Spin-one systems 200 The classical limit 201 7.5 Addition of angular momenta 205 Case of two spin-half systems 210 Case of spin one and spin half 212 The classical limit 213 Problems 214 8 Hydrogen 220 8.1 Gross structure of hydrogen 221 Emission-line spectra 226 Radial eigenfunctions 226 Shielding 231 Expectation values for r k 234
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Contents vii 8.2 Fine structure and beyond 235 Spin-orbit coupling 236 Hyperfine structure 241 Problems 243 9 Perturbation theory 246 9.1 Time-independent perturbations 247 Quadratic Stark effect 249 Linear Stark effect and degenerate perturbation theory 250 Effect of an ex- ternal magnetic field 253 Paschen–Back effect 255 Zeeman effect 255 9.2 Variational principle 258 9.3 Time-dependent perturbation theory 260 Fermi golden rule 261 Radiative transition rates 262 Selection rules 267 Problems 269 10 Helium and the periodic table 273 10.1 Identical particles 273 Generalisation to the case of N identical particles 275 Pauli exclusion principle 275 10.2 Gross structure of helium 277 Gross structure from perturbation theory 278 Application of the variational principle to he- lium 280 Excited states of helium 281 Electronic configurations and spectroscopic terms 285 Spectrum of helium 286 10.3 The periodic table 286 From lithium to argon 286 The fourth and fifth peri- ods 291 Problems 293 11 Adiabatic principle 295 11.1 Derivation of the adiabatic principle 296 11.2 Application to kinetic theory 298 11.3 Application to thermodynamics 301 11.4 The compressibility of condensed matter 303 11.5 Covalent bonding 304 A toy model of a covalent bond 305 Molecular dynam- ics 307 Dissociation of molecules 308 11.6 The WKBJ approximation 309 Problems 310 12 Scattering Theory 313 12.1 The scattering operator 314 Perturbative treatment of the scattering operator 316 12.2 The S-matrix 318 The i ǫ prescription 319 Expanding the S-matrix 321 The scattering amplitude 324 12.3 Cross-sections and scattering experiments 326 The optical theorem 330 12.4 Scattering electrons off hydrogen 332 12.5 Partial wave expansions 334 Scattering at low energy 339 12.6 Resonances 341 Breit–Wigner resonances 344 Radioactive decay 345 Problems 347
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viii Contents Appendices A Cartesian tensors 349 B Fourier series and transforms 351 C Operators in classical statistical mechanics 353 D Lorentz covariant equations 356 E Thomas precession 358 F Matrix elements for a dipole-dipole interaction 361 G Selection rule for j 363 H Restrictions on scattering potentials 364 Index 365
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Preface This book grew out of classes given for many years to the second-year un- dergraduates of Merton College, Oxford. The University lectures that the students were attending in parallel were restricted to the wave-mechanical methods introduced by Schr¨odinger, with a very strong emphasis on the time-independent Schr¨odinger equation. The classes had two main aims: to introduce more wide-ranging concepts associated especially with Dirac and
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