- Preface
- Introduction: The Stern-Gerlach Experiment
- I. The Structure of Quantum Theory

- 1. Vector Spaces

- Vectors
- Operators
- Eigenvectors and Eigenvalues
- Inner Products of Vectors in R²
- Complex Numbers
- The Space C2
- The Pauli Spin Matrices
- Mathematical Generalization
- Vector Spaces
- Linear Operators
- Inner Products on V
- Subspaces and Projection Operators
- Orthonormal Bases
- Operators with a Discrete Spectrum
- Operators with a Continuous Spectrum
- Hilbert Spaces

- 2. States and Observables in Quantum Mechanics

- Classical Mechanics: Systems and Their States
- Observables and Experimental Questions
- States and Observables in Quantum Theory
- Probabilities and Expectation Values
- The Evolution of States in Classical Mechanics
- Determinism
- The Evolution of States in Quantum Mechanics
- Theories and Models

- 3. Physical Theory and Hilbert Spaces

- Minimal Assumptions for Physical Theory
- The Representation of Outcomes and Events
- The Representation of States
- Determinism, Indeterminism, and the Principle of Superposition
- Mixed States
- Observables and Operators
- Relations between Observables: Functional Dependence and Compatibility Incompatible Observables
- The Representational Capacity of Hilbert Spaces
- The Schrödinger Equation

- 4. Spin and Its Representation

- Symmetry Conditions and Spin States
- A Partial Representation of Spin in R2
- The Representation of (Sa) in C2
- Conclusion

- 5. Density Operators and Tensor-Product Spaces

- Operators of the Trace Class
- Density Operators
- Density Operators on C2
- Pure and Mixed States
- The Dynamical Evolution of States
- Gleason’s Theorem
- Composite Systems and Tensor-Product Spaces
- The Reduction of States of Composite Systems

- 1. Vector Spaces
- II. The Interpretation of Quantum Theory

- 6. The Problem of Properties

- Properties, Experimental Questions, and the Dispersion Principle
- The EPR Argument
- Bohm’s Version of the EPR Experiment
- The Statistical Interpretation
- Kochen and Specker’s Example
- Generalizing the Problem
- The Bell-Wigner Inequality
- Hidden Variables
- Interpreting Quantum Theory: Statistical States and Value States

- 7. Quantum Logic

- The Algebra of Properties of a Simple Classical System
- Boolean Algebras
- Posets and Lattices
- The Structure of S(H)
- The Algebra of Events
- A Formal Approach to Quantum Logic
- An Unexceptionable Interpretation of Quantum Logic
- Putnam on Quantum Logic
- Properties and Deviant Logic

- 8. Probability, Causality, and Explanation

- Probability Generalized
- Two Uniqueness Results
- The Two-Slit Experiment: Waves and Particles
- The Two-Slit Experiment: Conditional Probabilities
- The Bell-Wigner Inequality and Classical Probability
- Bell Inequalities and Einstein-Locality
- Bell Inequalities and Causality
- Coupled Systems and Conditional Probabilities
- Probability, Causality, and Explanation

- 9. Measurement

- Three Principles of Limitation
- Indeterminacy and Measurement
- Projection Postulates
- Measurement and Conditionalization
- The Measurement Problem and Schrodinger’s Cat
- Jauch’s Model of the Measurement Process
- A Problem for Internal Accounts of Measurement
- Three Accounts of Measurement

- 10. An Interpretation of Quantum Theory

- Abstraction and Interpretation
- Properties and Latencies: The Quantum Event Interpretation
- The Copenhagen Interpretation
- The Priority of the Classical World
- Quantum Theory and the Classical Horizon

- 6. The Problem of Properties
- Appendix A. Gleason’s Theorem
- Appendix B. The Lÿders Rule
- Appendix C. Coupled Systems and Conditionalization
- References
- Index

# The Structure and Interpretation of Quantum Mechanics

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ISBN 9780674843929

Publication Date: 03/01/1992