Modern Quantum Mechanics

TOC\r......Page 7
Foreword to the First Edition......Page 11
Preface to the Revised Edition......Page 13
Preface to the Second Edition......Page 15
In Memoriam......Page 19
1.1 The Stem-Gerlach Experiment......Page 21
1.2 Kets, Bras, and Operators......Page 30
1.3 Base Kets and Matrix Representations......Page 37
1.4 Measurements, Observables, and the Uncertainty Relations......Page 43
1.5 Change of Basis......Page 55
1.6 Position, Momentum, and Translation......Page 60
1.7 Wave Functions in Position and Momentum Space......Page 70
2.1 Time-Evolution and the Schrodinger Equation......Page 86
2.2 The Schrodinger Versus the Heisenberg Picture......Page 100
2.3 Simple Harmonic Oscillator......Page 109
2.4 Schrodinger\'s Wave Equation......Page 117
2.5 Elementary Solutions to SchrOdinger\'s Wave Equation......Page 123
2.6 Propagators and Feynman Path Integrals......Page 136
2.7 Potentials and Gauge Transformations......Page 149
3 Theory of Angular Momentum......Page 177
3.1 Rotations and Angular-Momentum Commutation Relations 1......Page 77
3.2 Spin 1/2 Systems and Finite Rotations......Page 183
3.3 SO(3), SU(2), and Euler Rotations......Page 192
3.4 Density Operators and Pure Versus Mixed Ensembles......Page 198
3.5 Eigenvalues and Eigenstates of Angular Momentum......Page 211
3.6 Orbital Angular Momentum......Page 219
3.7 Schrodinger\'s Equation for Central Potentials......Page 227
3.8 Addition of Angular Momenta......Page 237
3.9 Schwinger\'s Oscillator Model of Angular Momentum......Page 252
3.10 Spin Correlation Measurements and Bell\'s Inequality......Page 258
3.11 Tensor Operators......Page 266
4.1 Symmetries, Conservation Laws, and Degeneracies......Page 282
4.2 Discrete Symmetries, Parity, or Space Inversion......Page 289
4.3 Lattice Translation as a Discrete Symmetry......Page 300
4.4 The Time-Reversal Discrete Symmetry......Page 304
5.1 Time-Independent Perturbation Theory: Nondegenerate Case......Page 323
5.2 Time-Independent Perturbation Theory: The Degenerate Case......Page 336
5.3 Hydrogen-Like Atoms: Fine Structure and the Zeeman Effect......Page 341
5.4 Variational Methods......Page 352
5.5 Time-Dependent Potentials: The Interaction Picture......Page 356
5.6 Hamiltonians with Extreme Time Dependence......Page 365
5.7 Time-Dependent Perturbation Theory......Page 375
5.8 Applications to Interactions with the Classical Radiation Field......Page 385
5.9 Energy Shift and Decay Width......Page 391
6.1 Scattering as a Time-Dependent Perturbation......Page 406
6.2 The Scattering Amplitude......Page 411
6.3 The Born Approximation......Page 419
6.4 Phase Shifts and Partial Waves......Page 424
6.5 Eikonal Approximation......Page 437
6.6 Low-Energy Scattering and Bound States......Page 443
6.7 Resonance Scattering......Page 450
6.8 Symmetry Considerations in Scattering......Page 453
6.9 Inelastic Electron-Atom Scattering......Page 456
7.1 Permutation Symmetry......Page 466
7.2 Symmetrization Postulate......Page 470
7.3 Two-Electron System......Page 472
7.4 The Helium Atom......Page 475
7.5 Multiparticle States......Page 479
7.6 Quantization of the Electromagnetic Field......Page 492
8.1 Paths to Relativistic Quantum Mechanics......Page 506
8.2 The Dirac Equation......Page 514
8.3 Symmetries of the Dirac Equation......Page 521
8.4 Solving with a Central Potential......Page 526
8.5 Relativistic Quantum Field Theory......Page 534
A.1 Coulomb\'s Law, Charge, and Current......Page 539
A.2 Converting Between Systems......Page 540
B.1 Free Particles (V = 0)......Page 543
B.2 Piecewise Constant Potentials in One Dimension......Page 544
B.3 Transmission-Reflection Problems......Page 545
B.4 Simple Harmonic Oscillator......Page 546
B.5 The Central Force Problem [Spherically Symmetrical Potential V = V(r)]......Page 547
B.6 Hydrogen Atom......Page 551
C Proof of the Angular-Momentum Addition Rule Given by Equation (3.8.38)......Page 553
Bibliography......Page 555
Index......Page 557