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