PRINCIPLES OF QUANTUM MECHANICSPDF电子书下载

1. Mathematical Introduction 1

1.1. Linear Vector Spaces：Basics 1

1.2. Inner Product Spaces 7

1.3. The Dirac Notation 13

1.4. Subspaces 20

1.5. Linear Operators 21

1.6. Matrix Elements of Linear Operators 23

1.7. Active and Passive Transformations 32

1.8. The Eigenvalue Problem 33

1.9. Functions of Operators and Related Concepts 58

1.10. Generalization to Infinite Dimensions 61

2. Review of Classical Mechanics 79

2.1. The Principle of Least Action and Lagrangian Mechanics 79

2.2. The Electromagnetic Lagrangian 88

2.3. The Two-Body Problem 89

2.4. How Smart Is a Particle？ 91

2.5. The Hamiltonian Formalism 91

2.6. The Electromagnetic Force in the Hamiltonian Scheme 95

2.7. Cyclic Coordinates，Poisson Brackets，and Canonical Transformations 96

2.8. Symmetries and Their Consequences 104

3. All Is Not Well with Classical Mechanics 111

3.1. Particles and Waves in Classical Physics 111

3.2. An Experiment with Waves and Particles（Classical） 112

3.3. The Double-Slit Experiment with Light 115

3.4. Matter Waves（de Broglie Waves） 117

3.5. Conclusions 118

4. The Postulates——A General Discussion 119

4.1. The Postulates 119

4.2. Discussion of Postulates Ⅰ-Ⅲ 121

4.3. The Schrodinger Equation 151

5. Simple Problems in One Dimension 159

5.1. The Free Particle 159

5.2. The Particle in a Box 165

5.3. The Continuity Equation for Probability 174

5.4. The Single-Step Potential：A Problem in Scattering 177

5.5. The Double-Slit Experiment 186

5.6. Some Theorems 186

6. The Classical Limit 189

7. The Harmonic Oscillator 195

7.1. Why Study the Harmonic Oscillator？ 195

7.2. Review of the Classical Oscillator 199

7.3. Quantization of the Oscillator（Coordinate Basis） 199

7.4. The Oscillator in the Energy Basis 214

7.5. Passage from the Energy Basis to the X Basis 227

8. The Path Integral Formulation of Quantum Theory 233

8.1. The Path Integral Recipe 233

8.2. Analysis of the Recipe 234

8.3. An Approximation to U（t）for the Free Particle 235

8.4. Path Integral Evaluation of the Free-Particle Propagator 237

8.5. Equivalence to the Schrodinger Equation 240

8.6. Potentials of the form V＝ a＋bx＋cx2＋dx＋exx 242

9. The Heisenberg Uncertainty Relations 245

9.1. Introduction 245

9.2. Derivation of the Uncertainty Relations 245

9.3. The Minimum Uncertainty Packet 247

9.4. Applications of the Uncertainty Principle 249

9.5. The Energy-Time Uncertainty Relation 252

10. Systems with N Degrees of Freedom 255

10.1. N Particles in One Dimension 255

10.2. More Particles in More Dimensions 267

10.3. Identical Particles 268

11. Symmetries and Their Consequences 289

11.1. Overview 289

11.2. Translational Invariance in Quantum Theory 289

11.3. Time Translational Invariance 305

11.4. Parity Invariance 307

12. Rotational Invariance and Angular Momentum 313

12.1. Translations in Two Dimensions 313

12.2. Rotations in Two Dimensions 314

12.3. The Eigenvalue Problem of L2 321

12.4. Angular Momentum in Three Dimensions 326

12.5. The Eigenvalue Problem of L2 and Lz 330

12.6. Solution of Rotationally Invariant Problems 349

13. The Hydrogen Atom 363

13.1. The Eigenvalue Problem 363

13.2. The Degeneracy of the Hydrogen Spectrum 369

13.3. Numerical Estimates and Comparison with Experiment 371

13.4. Multielectron Atoms and the Periodic Table 379

14. Spin 383

14.1. Introduction 383

14.2. What is the Nature of Spin？ 383

14.3. Kinematics of Spin 384

14.4. Spin Dynamics 396

14.5. Return of Orbital Degrees of Freedom 408

15. Addition of Angular Momenta 413

15.1. A Simple Example 413

15.2. The General Problem 418

15.3. Irreducible Tensor Operators 426

15.4. Explanation of Some “Accidental” Degeneracies 432

16. Variational and WKB Methods 439

16.1. The Variational Method 439

16.2. The Wentzel-Kramers-Brillouin Method 446

17. Time-Independent Perturbation Theory 459

17.1. The Formalism 459

17.2. Some Examples 462

17.3. Degenerate Perturbation Theory 473

18. Time-Dependent Perturbation Theory 481

18.1. The Problem 481

18.2. First-Order Perturbation Theory 482

18.3. Higher Orders in Perturbation Theory 492

18.4. A General Discussion of the Electromagnetic Interactions 501

18.5. Interaction of Atoms with Electromagnetic Radiation 508

19. Scattering Theory 533

19.1. Introduction 533

19.2. Recapitulation of One-Dimensional Scattering and Overview 534

19.3. The Born Approximation（Time-Dependent Description） 540

19.4. Born Again（Time-Independent Approximation） 545

19.5. The Partial Wave Expansion 556

19.6. Two-Particle Scattering 567

20. The Dirac Equation 575

20.1. The Free-Particle Dirac Equation 575

20.2. Electromagnetic Interaction of the Dirac Particle 578

20.3. More on Relativistic Quantum Mechanics 586

Appendix 593

A.1.Matrix Inversion 593

A.2.Gaussian Integrals 596

A.3.Complex Numbers 598

ANSWERS TO SELECTED EXERCISES 601

TABLE OF CONSTANTS 605

INDEX 607