Contents 13 Two-level problems 223 13.1 Time-independent problems 223 132 Time-dependent problems 234 13.3 Problems 246 14 Spin systems in the presence of magnetic fields 141 Constant magnetic field 251 14.2 Spin precession 14.3 Time-dependent magnetic field:spin magnetic resonance 14.4 Problems 258 15 Oscillation and regeneration in neutrinos and neutral K-mesons as two-level systems 15.1 Neutrinos 260 15.2 The solar neutrino puzzle 260 Neutrino oscillations 5 Decay and regeneration 15.5 Oscillation and regeneration of stable and unstable systems 269 15.6 Neutral &-mesons 273 15.7 Problems 276 16 Time-independent perturbation for bound states 16.1 Basic formalism 277 16.2 Harm nic oscilla r:perturbative vs.exact results l63 Second-order Stark effect 16.4 Degenerate states 287 165 Linear Stark effect 289 16.6 Problems 290 17 Time-dependent perturbation 293 17.1 Basic formalism 293 17.2 Harmonic perturbation and Fermi's golden rule 17 Transitions into a group of states and scattering cross-section 286 17.4 Resonance and decav 30 17.5 Appendix to Chapter 17 310 17.6 Problems 315 18 Interaction of charged particles and radiation in perturbation theory 318 18.1 Electron in an electromagnetic field:the absorption cross-section 318 182 18.3 Coulomb excitations of an atom 184 lonization 328 18.5 Thomson.Ravleigh.and raman scattering in second-order perturbation 331 18.6 Problems 339x Contents 13 Two-level problems 223 13.1 Time-independent problems 223 13.2 Time-dependent problems 234 13.3 Problems 246 14 Spin ½ systems in the presence of magnetic fields 251 14.1 Constant magnetic field 251 14.2 Spin precession 254 14.3 Time-dependent magnetic field: spin magnetic resonance 255 14.4 Problems 258 15 Oscillation and regeneration in neutrinos and neutral K-mesons as two-level systems 260 15.1 Neutrinos 260 15.2 The solar neutrino puzzle 260 15.3 Neutrino oscillations 263 15.4 Decay and regeneration 265 15.5 Oscillation and regeneration of stable and unstable systems 269 15.6 Neutral K-mesons 273 15.7 Problems 276 16 Time-independent perturbation for bound states 277 16.1 Basic formalism 277 16.2 Harmonic oscillator: perturbative vs. exact results 281 16.3 Second-order Stark effect 284 16.4 Degenerate states 287 16.5 Linear Stark effect 289 16.6 Problems 290 17 Time-dependent perturbation 293 17.1 Basic formalism 293 17.2 Harmonic perturbation and Fermi’s golden rule 296 17.3 Transitions into a group of states and scattering cross-section 299 17.4 Resonance and decay 303 17.5 Appendix to Chapter 17 310 17.6 Problems 315 18 Interaction of charged particles and radiation in perturbation theory 318 18.1 Electron in an electromagnetic field: the absorption cross-section 318 18.2 Photoelectric effect 323 18.3 Coulomb excitations of an atom 325 18.4 Ionization 328 18.5 Thomson, Rayleigh, and Raman scattering in second-order perturbation 331 18.6 Problems 339