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The Structure and Interpretation of Quantum Mechanics

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PAPERBACK

$50.00 • £40.95 • €45.00

ISBN 9780674843929

Publication Date: 03/01/1992

Short

384 pages

6-1/8 x 9-1/4 inches

71 line illustrations

World

Related Subjects

  • 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
  • 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
  • Appendix A. Gleason’s Theorem
  • Appendix B. The Lÿders Rule
  • Appendix C. Coupled Systems and Conditionalization
  • References
  • Index

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