Modern quantum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Reading, Mass. [u.a.]
Addison-Wesley
2008
|
| Ausgabe: | Rev. ed., [Nachdr.] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 500 S. graph. Darst. |
| ISBN: | 0201539292 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Modern quantum mechanics
Autor: Sakurai, Jun J.
Jahr: 2008
Contents
Foreword iii
Preface iv
In Memoriam vii
1 FUNDAMENTAL CONCEPTS 1
1.1 The Stem-Gerlach Experiment 2
1.2 Kets, Bras, and Operators 10
1.3 Base Kets and Matrix Representations 17
1.4 Measurements, Observables, and the Uncertainty Relations 23
1.5 Change of Basis 36
1.6 Position, Momentum, and Translation 41
1.7 Wave Functions in Position and Momentum Space 51
Problems 60
2 QUANTUM DYNAMICS 68
2.1 Time Evolution and the Schrodinger Equation 68
2.2 The Schrodinger Versus the Heisenberg Picture 80
2.3 Simple Harmonic Oscillator 89
2.4 Schrodinger s Wave Equation 97
2.5 Propagators and Feynman Path Integrals 109
2.6 Potentials and Gauge Transformations 123
Problems 143
3 THEORY OF ANGULAR MOMENTUM 152
3.1 Rotations and Angular Momentum Commutation Relations 152
3.2 Spin 1/2 Systems and Finite Rotations 158
3.3 SO(3), SU(2), and Euler Rotations 168
3.4 Density Operators and Pure Versus Mixed Ensembles 174
3.5 Eigenvalues and Eigenstates of Angular Momentum 187
3.6 Orbital Angular Momentum 195
3.7 Addition of Angular Momenta 203
3.8 Schwinger s Oscillator Model of Angular Momentum 217
3.9 Spin Correlation Measurements and Bell s Inequality 223
3.10 Tensor Operators 232
Problems 242
4 SYMMETRY IN QUANTUM MECHANICS 248
4.1 Symmetries, Conservation Laws, and Degeneracies 248
4.2 Discrete Symmetries, Parity, or Space Inversion 251
4.3 Lattice Translation as a Discrete Symmetry 261
4.4 The Time-Reversal Discrete Symmetry 266
Problems 282
IX
x Contents
5 APPROXIMATION METHODS 285
5.1 Time-Independent Perturbation Theory:
Nondegenerate Case 285
5.2 Time-Independent Perturbation Theory:
The Degenerate Case 298
5.3 Hydrogenlike Atoms: Fine Structure and the Zeeman Effect 304
5.4 Variational Methods 313
5.5 Time-Dependent Potentials: The Interaction Picture 316
5.6 Time-Dependent Perturbation Theory 325
5.7 Applications to Interactions with the Classical
Radiation Field 335
5.8 Energy Shift and Decay Width 341
Problems 345
6 IDENTICAL PARTICLES 357
6.1 Permutation Symmetry 357
6.2 Symmetrization Postulate 361
6.3 Two-Electron System 363
6.4 The Helium Atom 366
6.5 Permutation Symmetry and Young Tableaux 370
Problems 377
7 SCATTERING THEORY 379
7.1 The Lippmann-Schwinger Equation 379
7.2 The Born Approximation 386
7.3 Optical Theorem 390
7.4 Eikonal Approximation 392
7.5 Free-Particle States: Plane Waves Versus Spherical Waves 395
7.6 Method of Partial Waves 399
7.7 Low-Energy Scattering and Bound States 410
7.8 Resonance Scattering 418
7.9 Identical Particles and Scattering 421
7.10 Symmetry Considerations in Scattering 422
7.11 Time-Dependent Formulation of Scattering 424
7.12 Inelastic Electron-Atom Scattering 429
7.13 Coulomb Scattering 434
Problems 441
Appendix A 446
Appendix B 456
Appendix C 458
Supplement I Adiabatic Change and Geometrical Phase 464
Supplement II Non-Exponential Decays 481
Bibliography 487
Index 491
|
| adam_txt |
Titel: Modern quantum mechanics
Autor: Sakurai, Jun J.
Jahr: 2008
Contents
Foreword iii
Preface iv
In Memoriam vii
1 FUNDAMENTAL CONCEPTS 1
1.1 The Stem-Gerlach Experiment 2
1.2 Kets, Bras, and Operators 10
1.3 Base Kets and Matrix Representations 17
1.4 Measurements, Observables, and the Uncertainty Relations 23
1.5 Change of Basis 36
1.6 Position, Momentum, and Translation 41
1.7 Wave Functions in Position and Momentum Space 51
Problems 60
2 QUANTUM DYNAMICS 68
2.1 Time Evolution and the Schrodinger Equation 68
2.2 The Schrodinger Versus the Heisenberg Picture 80
2.3 Simple Harmonic Oscillator 89
2.4 Schrodinger's Wave Equation 97
2.5 Propagators and Feynman Path Integrals 109
2.6 Potentials and Gauge Transformations 123
Problems 143
3 THEORY OF ANGULAR MOMENTUM 152
3.1 Rotations and Angular Momentum Commutation Relations 152
3.2 Spin 1/2 Systems and Finite Rotations 158
3.3 SO(3), SU(2), and Euler Rotations 168
3.4 Density Operators and Pure Versus Mixed Ensembles 174
3.5 Eigenvalues and Eigenstates of Angular Momentum 187
3.6 Orbital Angular Momentum 195
3.7 Addition of Angular Momenta 203
3.8 Schwinger's Oscillator Model of Angular Momentum 217
3.9 Spin Correlation Measurements and Bell's Inequality 223
3.10 Tensor Operators 232
Problems 242
4 SYMMETRY IN QUANTUM MECHANICS 248
4.1 Symmetries, Conservation Laws, and Degeneracies 248
4.2 Discrete Symmetries, Parity, or Space Inversion 251
4.3 Lattice Translation as a Discrete Symmetry 261
4.4 The Time-Reversal Discrete Symmetry 266
Problems 282
IX
x Contents
5 APPROXIMATION METHODS 285
5.1 Time-Independent Perturbation Theory:
Nondegenerate Case 285
5.2 Time-Independent Perturbation Theory:
The Degenerate Case 298
5.3 Hydrogenlike Atoms: Fine Structure and the Zeeman Effect 304
5.4 Variational Methods 313
5.5 Time-Dependent Potentials: The Interaction Picture 316
5.6 Time-Dependent Perturbation Theory 325
5.7 Applications to Interactions with the Classical
Radiation Field 335
5.8 Energy Shift and Decay Width 341
Problems 345
6 IDENTICAL PARTICLES 357
6.1 Permutation Symmetry 357
6.2 Symmetrization Postulate 361
6.3 Two-Electron System 363
6.4 The Helium Atom 366
6.5 Permutation Symmetry and Young Tableaux 370
Problems 377
7 SCATTERING THEORY 379
7.1 The Lippmann-Schwinger Equation 379
7.2 The Born Approximation 386
7.3 Optical Theorem 390
7.4 Eikonal Approximation 392
7.5 Free-Particle States: Plane Waves Versus Spherical Waves 395
7.6 Method of Partial Waves 399
7.7 Low-Energy Scattering and Bound States 410
7.8 Resonance Scattering 418
7.9 Identical Particles and Scattering 421
7.10 Symmetry Considerations in Scattering 422
7.11 Time-Dependent Formulation of Scattering 424
7.12 Inelastic Electron-Atom Scattering 429
7.13 Coulomb Scattering 434
Problems 441
Appendix A 446
Appendix B 456
Appendix C 458
Supplement I Adiabatic Change and Geometrical Phase 464
Supplement II Non-Exponential Decays 481
Bibliography 487
Index 491 |
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