《运算量子物理学》求取 ⇩

Prologue1

Ⅰ．Introduction5

1．Observables as POV Measures5

1.1．Statistical Analysis of an Experiment5

1.2．POV Measures Arising from Actual Measurements7

1.3．onceptual Problems Requiring POV Measures12

1.4．ew Possibilities Envisaged with POV Measures16

2．Historical Survey17

Ⅱ．Theory19

1．Hilbert Space Frame19

1.1．Preliminaries19

1.2．States and Observables23

2．Physical and Mathematical Features of POV Measures25

2.1．Unsharp Properties25

2.2．Coexistence26

2.3．Constructing POV Measures from PV Measures29

2.4．Neumark's Theorem31

2.5．Symmetric Operators and Contractions32

3． Quantum Measurement Theory34

3.1．Operations35

3.2．State Transformers37

3.3．Measurements39

3.4．The Standard Model42

3.5．Repeatable Measurements44

4．Individual Interpretation of Quantum Mechanics46

Ⅲ．Observables49

1．Observables as Covariant Objects50

2．Position and Momentum53

2.1．Covariance Properties53

2.2．Sharp Position and Momentum55

2.3．Unsharp Position and Momentum59

2.4．Phase Space Observables60

3．Angular Momentum and Angle65

3.1．Covariance Properties65

3.2．Orbital Angular Momentum67

3.3．Spin70

3.4．Angle Observables73

4．Energy and Time77

4.1．Energy78

4.2．Time79

5．Photon Observables82

5.1．Photon Number and Phase82

5.2．Joint Observables for the Quadrature Components88

5.3．Photon Localisation92

Ⅳ．Measurements95

1．Continuous Observables95

2．Pairs of Observables101

2.1．Coexistent Observables101

2.2．Examples102

2.3．Complementary Observables104

2.4．Coupling Properties of Position and Momentum107

2.5．The Heisenberg Interpretation of the Uncertainty Relations108

2.6．Coexistence of Complementary Spin Observables109

3．Measurements and Conservation Laws110

3.1．Repeatable Measurements and Conservation Laws111

3.2．Spin Measurements and Rotation Invariance112

3.3．Position Measurements and Momentum Conservation114

Ⅴ．Uncertainty117

1．Coarse-Graining118

2．Informational Completeness120

3．Unsharpness124

3.1．Quantum Indeterminism and Classicality Conditions124

3.2．Measurement:Disturbance Versus Information Gain127

3.3．Unsharpness in Phase Space Inference128

3.4．Impossibility of Individual State Determination131

4．Uncertainty Relations134

4.1．Variance134

4.2．Alternative Measures of Uncertainty137

4.3．Entropy139

Ⅵ．Phase Space145

1．Representations of States as Phase Space Functions145

2．Joint Position-Momentum Measurement150

2.1．The Model151

2.2．Indeterminacy Relations152

2.3．Mutual Disturbance154

2.4．Repeatability Features155

3．Classical Limit156

3.1．Classical Measurement Situation156

3.2．Approximately Ideal Measurements159

Ⅶ．Experiments165

1．Stern-Gerlach Experiment165

1.1．Ideal Field167

1.2．Realistic Magnetic Field171

1.3．Proper Screen Observables173

2．Informationally Complete Polarisation Measurement174

3．Measurement Schemes Involving Photons177

3.1．Photon Counting and a Lossless Beam Splitter177

3.2．First Kind Measurements of the Photon Number180

3.3．Measurement of the Photon Number in a Microwave Cavity186

3.4．Phase Distributions from Number Statistics189

3.5．Nondegenerate Amplification and Two-Mode Squeezing191

3.6．Homodyne Detection192

3.7．Joint Measurement of the Quadrature Components195

3.8．Atomic Position Measurement197

4． Wave-Particle Duality of Photons199

4.1．Photon Split-Beam Experiments200

4.2．Joint Path-Interference Measurements for Single Photons206

Epilogue213

References215

Notations225

Subject Index227