量子力学 英文

Introduction 1

Part Ⅰ Basic features of quantum mechanics 7

1 From classical mechanics to quantum mechanics 7

1.1 Review of the foundations of classical mechanics 7

1.2 An interferometry experiment and its consequences 12

1.3 State as vector 20

1.4 Quantum probability 28

1.5 The historical need of a new mechanics 31

Summary 40

Problems 41

Further reading 42

2 Quantum observables and states 43

2.1 Basic features of quantum observables 43

2.2 Wave function and basic observables 68

2.3 Uncertainty relation 82

2.4 Quantum algebra and quantum logic 92

Summary 96

Problems 97

Further reading 99

3 Quantum dynamics 100

3.1 The Schr？dinger equation 101

3.2 Properties of the Schr？dinger equation 107

3.3 Schr？dinger equation and Galilei transformations 111

3.4 One-dimensional free particle in a box 113

3.5 Unitary transformations 117

3.6 Different pictures 125

3.7 Time derivatives and the Ehrenfest theorem 129

3.8 Energy-time uncertainty relation 130

3.9 Towards a time operator 135

Summary 138

Problems 139

Further reading 140

4 Examples of quantum dynamics 141

4.1 Finite potential wells 141

4.2 Potential barrier 145

4.3 Tunneling 150

4.4 Harmonic oscillator 154

4.5 Quantum particles in simple fields 165

Summary 169

Problems 170

5 Density matrix 174

5.1 Basic formalism 174

5.2 Expectation values and measurement outcomes 177

5.3 Time evolution and density matrix 179

5.4 Statistical properties of quantum mechanics 180

5.5 Compound systems 181

5.6 Pure-and mixed-state representation 187

Summary 188

Problems 189

Further reading 190

Part Ⅱ More advanced topics 193

6 Angular momentum and spin 193

6.1 Orbital angular momentum 193

6.2 Special examples 207

6.3 Spin 217

6.4 Composition of angular momenta and total angular momentum 226

6.5 Angular momentum and angle 239

Summary 241

Problems 242

Further reading 244

7 Identical particles 245

7.1 Statistics and quantum mechanics 245

7.2 Wave function and symmetry 247

7.3 Spin and statistics 249

7.4 Exchange interaction 254

7.5 Two recent applications 255

Summary 257

Problems 257

Further reading 258

8 Symmetries and conservation laws 259

8.1 Quantum transformations and symmetries 259

8.2 Continuous symmetries 264

8.3 Discrete symmetries 266

8.4 A brief introduction to group theory 267

Summary 275

Problems 275

Further reading 276

9 The measurement problem in quantum mechanics 277

9.1 Statement of the problem 278

9.2 A brief history of the problem 284

9.3 Schr？dinger cats 291

9.4 Decoherence 297

9.5 Reversibility/irreversibility 308

9.6 Interaction-free measurement 315

9.7 Delayed-choice experiments 320

9.8 Quantum Zeno effect 322

9.9 Conditional measurements or postselection 325

9.10 Positive operator valued measure 327

9.11 Quantum non-demolition measurements 335

9.12 Decision and estimation theory 341

Summary 349

Problems 351

Further reading 353

Part Ⅲ Matter and light 357

10 Perturbations and approximation methods 357

10.1 Stationary perturbation theory 357

10.2 Time-dependent perturbation theory 366

10.3 Adiabatic theorem 369

10.4 The variational method 371

10.5 Classical limit 372

10.6 Semiclassical limit and WKB approximation 378

10.7 Scattering theory 384

10.8 Path integrals 389

Summary 398

Problems 399

Further reading 399

11 Hydrogen and helium atoms 401

11.1 Introduction 401

11.2 Quantum theory of the hydrogen atom 403

11.3 Atom and magnetic field 413

11.4 Relativistic corrections 423

11.5 Helium atom 426

11.6 Many-electron effects 431

Summary 436

Problems 437

Further reading 438

12 Hydrogen molecular ion 439

12.1 The molecular problem 439

12.2 Born-Oppenheimer approximation 440

12.3 Vibrational and rotational degrees of freedom 443

12.4 The Morse potential 447

12.5 Chemical bonds and further approximations 449

Summary 453

Problems 453

Further reading 454

13 Quantum optics 455

13.1 Quantization of the electromagnetic field 457

13.2 Thermodynamic equilibrium of the radiation field 462

13.3 Phase-number uncertainty relation 463

13.4 Special states of the electromagnetic field 465

13.5 Quasi-probability distributions 474

13.6 Quantum-optical coherence 481

13.7 Atom-field interaction 484

13.8 Geometric phase 497

13.9 The Casimir effect 501

Summary 506

Problems 507

Further reading 509

Part Ⅳ Quantum information:state and correlations 513

14 Quantum theory of open systems 513

14.1 General considerations 514

14.2 The master equation 516

14.3 A formal generalization 523

14.4 Quantum jumps and quantum trajectories 528

14.5 Quantum optics and Schr？dinger cats 533

Summary 540

Problems 541

Further reading 542

15 State measurement in quantum mechanics 544

15.1 Protective measurement of the state 544

15.2 Quantum cloning and unitarity violation 548

15.3 Measurement and reversibility 550

15.4 Quantum state reconstruction 554

15.5 The nature of quantum states 564

Summary 565

Problems 565

Further reading 566

16 Entanglement:non-separability 567

16.1 EPR 568

16.2 Bohm's version of the EPR state 573

16.3 HV theories 577

16.4 Bell's contribution 582

16.5 Experimental tests 595

16.6 Bell inequalities with homodyne detection 605

16.7 Bell theorem without inequalities 613

16.8 What is quantum non-locality？ 619

16.9 Further developments about inequalities 623

16.10 Conclusion 625

Summary 625

Problems 626

Further reading 627

17 Entanglement：quantum information and computation 628

17.1 Information and entropy 628

17.2 Entanglement and information 631

17.3 Measurement and information 639

17.4 Qubits 642

17.5 Teleportation 643

17.6 Quantum cryptography 646

17.7 Elements of quantum computation 650

17.8 Quantum algorithms and error correction 659

Summary 671

Problems 672

Further reading 673

Bibliography 674

Author index 710

Subject index 716