The quantum mechanics solver: how to apply quantum theory to modern physics

Cover......Page 1
The Quantum Mechanics Solver, 2nd Edition......Page 2
Preface to the Second Edition......Page 4
Contents......Page 7
1 Principles......Page 13
3 The Particular Case of a Point-Like Particle; Wave Mechanics......Page 16
4 Angular Momentum and Spin......Page 18
5 Exactly Soluble Problems......Page 19
6 Approximation Methods......Page 21
7 Identical Particles......Page 22
8 Time-Evolution of Systems......Page 23
9 Collision Processes......Page 24
Part I Elementary Particles, Nuclei and Atoms......Page 27
1 Neutrino Oscillations......Page 28
1.1 Mechanism of the Oscillations; Reactor Neutrinos......Page 29
1.2 Oscillations of Three Species; Atmospheric Neutrinos......Page 31
1.3 Solutions......Page 34
1.4 Comments......Page 38
2.1 The Hyperfine Splitting of the Ground State......Page 39
2.2 The Atomic Fountain......Page 41
2.4 The Drift of Fundamental Constants......Page 42
2.5 Solutions......Page 43
3 Neutron Interferometry......Page 47
3.1 Neutron Interferences......Page 48
3.2 The Gravitational Effect......Page 49
3.3 Rotating a Spin 1/2 by 360 Degrees......Page 50
3.4 Solutions......Page 52
4.1 Ramsey Fringes......Page 56
4.2 Solutions......Page 58
5.1 Preparation of the Neutron Beam......Page 63
5.3 The Stern–Gerlach Experiment......Page 65
5.4 Solutions......Page 67
6.1 Spin and Momentum Precession of an Electron in a Magnetic Field......Page 72
6.2 Solutions......Page 73
7.1 The Energy Balance in Tritium Decay......Page 76
7.2 Solutions......Page 77
7.3 Comments......Page 78
8.2 Hyperfine Splitting......Page 80
8.3 Zeeman Effect in the Ground State......Page 81
8.4 Decay of Positronium......Page 82
8.5 Solutions......Page 84
9 The Hydrogen Atom in Crossed Fields......Page 88
9.2 Pauli’s Result......Page 89
9.3 Solutions......Page 90
10.1 Energy Absorbed by One Atom......Page 93
10.2 Energy Loss in Matter......Page 94
10.3 Solutions......Page 96
10.4 Comments......Page 100
Part II Quantum Entanglement and Measurement......Page 102
11.1 The Electron Spin......Page 103
11.3 Correlations in the Singlet State......Page 104
11.4 A Simple Hidden Variable Model......Page 105
11.5 Bell’s Theorem and Experimental Results......Page 106
11.6 Solutions......Page 107
12.1 The Quasi-Classical States of a Harmonic Oscillator......Page 113
12.3 Quantum Superposition Versus Statistical Mixture......Page 115
12.4 The Fragility of a Quantum Superposition......Page 116
12.5 Solutions......Page 118
12.6 Comments......Page 123
13.1 Preliminaries......Page 125
13.2 Correlated Pairs of Spins......Page 126
13.3 The Quantum Cryptography Procedure......Page 129
13.4 Solutions......Page 130
14.1 Quantization of a Mode of the Electromagnetic Field......Page 134
14.2 The Coupling of the Field with an Atom......Page 136
14.3 Interaction of the Atom with an “Empty” Cavity......Page 137
14.4 Interaction of an Atom with a Quasi-Classical State......Page 138
14.5 Large Numbers of Photons: Damping and Revivals......Page 139
14.6 Solutions......Page 140
14.7 Comments......Page 147
15.1 Preliminaries: a von Neumann Detector......Page 149
15.2 Phase States of the Harmonic Oscillator......Page 150
15.4 An “Ideal” Measurement......Page 151
15.5 Solutions......Page 152
15.6 Comments......Page 155
16.1 Magnetic Resonance......Page 156
16.2 Ramsey Fringes......Page 157
16.3 Detection of the Neutron Spin State......Page 159
16.4 A Quantum Eraser......Page 160
16.5 Solutions......Page 161
16.6 Comments......Page 167
17.1 The Penning Trap in Classical Mechanics......Page 169
17.2 The Penning Trap in Quantum Mechanics......Page 170
17.3 Coupling of the Cyclotron and Axial Motions......Page 172
17.4 A Quantum Thermometer......Page 173
17.5 Solutions......Page 174
Part III Complex Systems......Page 183
18.1 The Two-Body Problem......Page 184
18.3 Relating the Three-Body and Two-Body Sectors......Page 185
18.5 From Mesons to Baryons in the Quark Model......Page 186
18.6 Solutions......Page 187
19.1 Particle in a Harmonic Trap......Page 192
19.2 Interactions Between Two Con.ned Particles......Page 193
19.4 Condensates with Repulsive Interactions......Page 194
19.5 Condensates with Attractive Interactions......Page 195
19.6 Solutions......Page 196
19.7 Comments......Page 201
20.1 The Molecule CsFeBr3......Page 202
20.3 Energy Levels of the Chain......Page 203
20.4 Vibrations of the Chain: Excitons......Page 205
20.5 Solutions......Page 207
21 A Quantum Box......Page 213
21.1 Results on the One-Dimensional Harmonic Oscillator......Page 214
21.2 The Quantum Box......Page 215
21.3 Quantum Box in a Magnetic Field......Page 216
21.4 Experimental Verification......Page 217
21.5 Anisotropy of a Quantum Box......Page 218
21.6 Solutions......Page 219
21.7 Comments......Page 227
22.1 Hydrocarbon Ions......Page 228
22.2 Nitrogenous Ions......Page 229
22.3 Solutions......Page 230
22.4 Comments......Page 232
23 Hyperfine Structure in Electron Spin Resonance......Page 233
23.2 Hyperfine Structure with Several Nuclei......Page 234
23.3 Experimental Results......Page 235
23.4 Solutions......Page 236
24 Probing Matter with Positive Muons......Page 241
24.1 Muonium in Vacuum......Page 242
24.2 Muonium in Silicon......Page 243
24.3 Solutions......Page 245
25.1 The Hydrogen Atom–Liquid Helium Interaction......Page 251
25.2 Excitations on the Surface of Liquid Helium......Page 253
25.4 The Sticking Probability......Page 254
25.5 Solutions......Page 255
25.6 Comments......Page 261
26.1 Optical Bloch Equations for an Atom at Rest......Page 262
26.2 The Radiation Pressure Force......Page 263
26.3 Doppler Cooling......Page 264
26.5 Solutions......Page 265
26.6 Comments......Page 271
27.2 Band Structure in a Periodic Potential......Page 272
27.3 The Phenomenon of Bloch Oscillations......Page 273
27.4 Solutions......Page 276
27.5 Comments......Page 280
Author Index......Page 281
Subject Index......Page 283