Prologue

Ⅰ．Introduction

1．Observables as POV Measures

1.1．Statistical Analysis of an Experiment

1.2．POV Measures Arising from Actual Measurements

1.3．onceptual Problems Requiring POV Measures

1.4．ew Possibilities Envisaged with POV Measures

2．Historical Survey

Ⅱ．Theory

1．Hilbert Space Frame

1.1．Preliminaries

1.2．States and Observables

2．Physical and Mathematical Features of POV Measures

2.1．Unsharp Properties

2.2．Coexistence

2.3．Constructing POV Measures from PV Measures

2.4．Neumark's Theorem

2.5．Symmetric Operators and Contractions

3． Quantum Measurement Theory

3.1．Operations

3.2．State Transformers

3.3．Measurements

3.4．The Standard Model

3.5．Repeatable Measurements

4．Individual Interpretation of Quantum Mechanics

Ⅲ．Observables

1．Observables as Covariant Objects

2．Position and Momentum

2.1．Covariance Properties

2.2．Sharp Position and Momentum

2.3．Unsharp Position and Momentum

2.4．Phase Space Observables

3．Angular Momentum and Angle

3.1．Covariance Properties

3.2．Orbital Angular Momentum

3.3．Spin

3.4．Angle Observables

4．Energy and Time

4.1．Energy

4.2．Time

5．Photon Observables

5.1．Photon Number and Phase

5.2．Joint Observables for the Quadrature Components

5.3．Photon Localisation

Ⅳ．Measurements

1．Continuous Observables

2．Pairs of Observables

2.1．Coexistent Observables

2.2．Examples

2.3．Complementary Observables

2.4．Coupling Properties of Position and Momentum

2.5．The Heisenberg Interpretation of the Uncertainty Relations

2.6．Coexistence of Complementary Spin Observables

3．Measurements and Conservation Laws

3.1．Repeatable Measurements and Conservation Laws

3.2．Spin Measurements and Rotation Invariance

3.3．Position Measurements and Momentum Conservation

Ⅴ．Uncertainty

1．Coarse-Graining

2．Informational Completeness

3．Unsharpness

3.1．Quantum Indeterminism and Classicality Conditions

3.2．Measurement:Disturbance Versus Information Gain

3.3．Unsharpness in Phase Space Inference

3.4．Impossibility of Individual State Determination

4．Uncertainty Relations

4.1．Variance

4.2．Alternative Measures of Uncertainty

4.3．Entropy

Ⅵ．Phase Space

1．Representations of States as Phase Space Functions

2．Joint Position-Momentum Measurement

2.1．The Model

2.2．Indeterminacy Relations

2.3．Mutual Disturbance

2.4．Repeatability Features

3．Classical Limit

3.1．Classical Measurement Situation

3.2．Approximately Ideal Measurements

Ⅶ．Experiments

1．Stern-Gerlach Experiment

1.1．Ideal Field

1.2．Realistic Magnetic Field

1.3．Proper Screen Observables

2．Informationally Complete Polarisation Measurement

3．Measurement Schemes Involving Photons

3.1．Photon Counting and a Lossless Beam Splitter

3.2．First Kind Measurements of the Photon Number

3.3．Measurement of the Photon Number in a Microwave Cavity

3.4．Phase Distributions from Number Statistics

3.5．Nondegenerate Amplification and Two-Mode Squeezing

3.6．Homodyne Detection

3.7．Joint Measurement of the Quadrature Components

3.8．Atomic Position Measurement

4． Wave-Particle Duality of Photons

4.1．Photon Split-Beam Experiments

4.2．Joint Path-Interference Measurements for Single Photons

Epilogue

References

Notations

Subject Index