运算量子物理学PDF电子书下载

Prologue 1

Ⅰ．Introduction 5

1．Observables as POV Measures 5

1.1．Statistical Analysis of an Experiment 5

1.2．POV Measures Arising from Actual Measurements 7

1.3．onceptual Problems Requiring POV Measures 12

1.4．ew Possibilities Envisaged with POV Measures 16

2．Historical Survey 17

Ⅱ．Theory 19

1．Hilbert Space Frame 19

1.1．Preliminaries 19

1.2．States and Observables 23

2．Physical and Mathematical Features of POV Measures 25

2.1．Unsharp Properties 25

2.2．Coexistence 26

2.3．Constructing POV Measures from PV Measures 29

2.4．Neumark's Theorem 31

2.5．Symmetric Operators and Contractions 32

3． Quantum Measurement Theory 34

3.1．Operations 35

3.2．State Transformers 37

3.3．Measurements 39

3.4．The Standard Model 42

3.5．Repeatable Measurements 44

4．Individual Interpretation of Quantum Mechanics 46

Ⅲ．Observables 49

1．Observables as Covariant Objects 50

2．Position and Momentum 53

2.1．Covariance Properties 53

2.2．Sharp Position and Momentum 55

2.3．Unsharp Position and Momentum 59

2.4．Phase Space Observables 60

3．Angular Momentum and Angle 65

3.1．Covariance Properties 65

3.2．Orbital Angular Momentum 67

3.3．Spin 70

3.4．Angle Observables 73

4．Energy and Time 77

4.1．Energy 78

4.2．Time 79

5．Photon Observables 82

5.1．Photon Number and Phase 82

5.2．Joint Observables for the Quadrature Components 88

5.3．Photon Localisation 92

Ⅳ．Measurements 95

1．Continuous Observables 95

2．Pairs of Observables 101

2.1．Coexistent Observables 101

2.2．Examples 102

2.3．Complementary Observables 104

2.4．Coupling Properties of Position and Momentum 107

2.5．The Heisenberg Interpretation of the Uncertainty Relations 108

2.6．Coexistence of Complementary Spin Observables 109

3．Measurements and Conservation Laws 110

3.1．Repeatable Measurements and Conservation Laws 111

3.2．Spin Measurements and Rotation Invariance 112

3.3．Position Measurements and Momentum Conservation 114

Ⅴ．Uncertainty 117

1．Coarse-Graining 118

2．Informational Completeness 120

3．Unsharpness 124

3.1．Quantum Indeterminism and Classicality Conditions 124

3.2．Measurement:Disturbance Versus Information Gain 127

3.3．Unsharpness in Phase Space Inference 128

3.4．Impossibility of Individual State Determination 131

4．Uncertainty Relations 134

4.1．Variance 134

4.2．Alternative Measures of Uncertainty 137

4.3．Entropy 139

Ⅵ．Phase Space 145

1．Representations of States as Phase Space Functions 145

2．Joint Position-Momentum Measurement 150

2.1．The Model 151

2.2．Indeterminacy Relations 152

2.3．Mutual Disturbance 154

2.4．Repeatability Features 155

3．Classical Limit 156

3.1．Classical Measurement Situation 156

3.2．Approximately Ideal Measurements 159

Ⅶ．Experiments 165

1．Stern-Gerlach Experiment 165

1.1．Ideal Field 167

1.2．Realistic Magnetic Field 171

1.3．Proper Screen Observables 173

2．Informationally Complete Polarisation Measurement 174

3．Measurement Schemes Involving Photons 177

3.1．Photon Counting and a Lossless Beam Splitter 177

3.2．First Kind Measurements of the Photon Number 180

3.3．Measurement of the Photon Number in a Microwave Cavity 186

3.4．Phase Distributions from Number Statistics 189

3.5．Nondegenerate Amplification and Two-Mode Squeezing 191

3.6．Homodyne Detection 192

3.7．Joint Measurement of the Quadrature Components 195

3.8．Atomic Position Measurement 197

4． Wave-Particle Duality of Photons 199

4.1．Photon Split-Beam Experiments 200

4.2．Joint Path-Interference Measurements for Single Photons 206

Epilogue 213

References 215

Notations 225

Subject Index 227