Contents 6.5 Interaction with the orbital angular momentum 125 Interaction with spin:intrinsic magnetic moment 126 Spin-orbit interaction 128 6.8 Aharonov-Bohm effect 129 6.9 Problems 7 Stern-Gerlach experiments 133 7.1 Experimental set-up and electron's magnetic moment 133 7.2 Discussion of the results 134 2 Problems 136 8 Some exactly solvable bound-state problems 137 8.1 Simple one-dimensional systems 137 8.2 Delta-function potential 145 Properties of a symmetric potential 147 8.4 The ammonia molecule 148 85 Periodic potentials 151 Problems in three dimensions 1 Simple systems . Hydrogen-like atom 16 89 Problems 70 9 Harmonic oscillator 174 9.1 Harmonic oscillator in one dimension 174 9.2 Problems 184 10 Coherent states 187 10.1 Eigenstates of the lowering operator 187 10.2 Coherent states and semiclassical description 192 10.3 Interaction of a harmonic oscillator with an electric field 194 104 Appendix to Chapter 10 10.5 Problems 200 11 Two-dimensional isotropic harmonic oscillator 203 11.1 The two-dimensional Har iltonian 11.2 Problems 207 2 Landau levels and quantum Hall effect 208 Landau levels in symmetric gauge 12.2 Wavefunctions for the LLL 212 12.3 Landau levels in Landau gauge 214 12.4 Quantum Hall effect 216 12. avefur ction for filled LLLs in a Fermi system 12.6 Problems ix Contents 6.5 Interaction with the orbital angular momentum 125 6.6 Interaction with spin: intrinsic magnetic moment 126 6.7 Spin–orbit interaction 128 6.8 Aharonov–Bohm effect 129 6.9 Problems 131 7 Stern–Gerlach experiments 133 7.1 Experimental set-up and electron’s magnetic moment 133 7.2 Discussion of the results 134 7.3 Problems 136 8 Some exactly solvable bound-state problems 137 8.1 Simple one-dimensional systems 137 8.2 Delta-function potential 145 8.3 Properties of a symmetric potential 147 8.4 The ammonia molecule 148 8.5 Periodic potentials 151 8.6 Problems in three dimensions 156 8.7 Simple systems 160 8.8 Hydrogen-like atom 164 8.9 Problems 170 9 Harmonic oscillator 174 9.1 Harmonic oscillator in one dimension 174 9.2 Problems 184 10 Coherent states 187 10.1 Eigenstates of the lowering operator 187 10.2 Coherent states and semiclassical description 192 10.3 Interaction of a harmonic oscillator with an electric field 194 10.4 Appendix to Chapter 10 199 10.5 Problems 200 11 Two-dimensional isotropic harmonic oscillator 203 11.1 The two-dimensional Hamiltonian 203 11.2 Problems 207 12 Landau levels and quantum Hall effect 208 12.1 Landau levels in symmetric gauge 208 12.2 Wavefunctions for the LLL 212 12.3 Landau levels in Landau gauge 214 12.4 Quantum Hall effect 216 12.5 Wavefunction for filled LLLs in a Fermi system 220 12.6 Problems 221