Cover
Title Page
Preface
Acknowledgments
Contents
1 Synopsis
2 The Quantum Entity and Quantum Mechanics
2.1 What Is a Classical Entity?
2.2 The Entity in Quantum Mechanics
2.3 Describing an Indeterminate Quantum Entity
2.4 The Copenhagen Quantum Postulate
2.5 Five Pillars of Quantum Mechanics
2.6 Degree of Freedom Space F
2.7 State Space V(F)
2.8 Operators O(F)
2.9 The Schrödinger Equation for State ψ(t,F)
2.10 Indeterminate Quantum Paths
2.11 The Process of Measurement
2.12 Summary: Quantum Entity
3 Quantum Mechanics: Empirical and Trans-empirical
3.1 Real Versus Exist
3.2 Empirical, Trans-empirical, and Indeterminate
3.3 Quantum Mechanics and the Trans-empirical
3.4 Quantum Degree of Freedom F Is Trans-empirical
3.5 The Quantum State ψ: Transition
3.6 Trans-empirical Domain and Laws of Physics
3.7 Quantum Superposition: Trans-empirical Paths
3.8 Trans-empirical Interpretation of Two-Slit Experiment
3.9 The Trans-empirical Quantum Principle
3.10 Does the Quantum State ψ(t,F) “Exist”?
3.11 Summary
4 Degree of Freedom F; State Space V
4.1 Dirac's Formulation of the Quantum State
4.2 State Space and Experiment
4.3 Quantum Degree of Freedom F
4.4 Binary Degree of Freedom and State Space
4.5 Degree of Freedom F_{(2N+1)}: State Space V_{(2N+1)}
4.6 Continuous Degree of Freedom
4.7 Basis States for State Space
4.8 Unitary Transformation: Momentum Basis
4.9 State Space V
4.10 Hilbert Space
4.11 Summary
5 Operators
5.1 Operators: Trans-empirical to Empirical
5.2 Hermitian Operators
5.3 Eigenstates: Projection Operators
5.4 Operators and Quantum Numbers
5.5 Periodic Degree of Freedom
5.6 Position and Momentum Operators x̂ and p̂
5.7 Heisenberg Commutation Equation
5.8 Expectation Value of Operators
5.9 The Schrödinger Equation
5.10 Heisenberg Operator Formulation
5.11 Summary
6 Density Matrix: Entangled States
6.1 Tensor Product
6.2 The Outer Product
6.3 Partial Trace for Outer Products
6.4 Density Matrix ρ
6.5 The Schmidt Decomposition
6.6 Reduced Density Matrix
6.7 Separable Quantum Systems
6.8 Entangled Quantum States
6.9 A Pair of Entangled Spins
6.10 Quantum Entropys
6.11 Pure and Mixed Density Matrix
6.12 Summary
7 Quantum Indeterminacy
7.1 The EPR Paradox
7.2 The Bell-CHSH Operator
7.3 Classical Probability: Objective Reality
7.4 The Bell Inequality
7.5 The Bell Inequality Non-violation
7.6 Bell Inequality Violation: Entangled States
7.7 The Bell–Kochen–Specker Inequality
7.8 Commuting and Non-commuting Operators
7.9 Quantum Probability
7.10 A Metaphor
7.11 Summary
8 Quantum Superposition
8.1 Superposing State Vectors
8.2 Probability and Probability Amplitudes
8.3 Empirical and Trans-Empirical Paths
8.4 Successive Slits
8.5 The Mach–Zehnder Interferometer
8.6 Determinate Empirical Paths: No Interference
8.7 Indeterminate Trans-Empirical Paths: Interference
8.8 Quantum Eraser
8.9 Erasing Interference
8.10 Restoring Interference
8.11 Partial Quantum Eraser
8.12 Summary
9 Quantum Theory of Measurement
9.1 Measurement: Trans-Empirical to Empirical
9.2 Position Projection Operator
9.3 Repeated Observations in Quantum Mechanics
9.4 Expectation Value of Projection Operators
9.5 The Experimental Device
9.6 The Process of Measurement
9.7 Mixed Density Matrix ρ_M
9.8 Reduced Density Matrix ρ_R
9.9 Preparation of a Quantum State
9.10 The Heisenberg Uncertainty Principle
9.11 Theories of Quantum Measurement
9.12 Summary
10 The Stern–Gerlach Experiment
10.1 The Experiment
10.2 Classical and Quantum Predictions
10.3 The Stern–Gerlach Hamiltonian
10.4 Electron's Time Evolution
10.5 Entanglement of Spin and Device
10.6 Summary of Spin Measurement
10.7 Irreversibility and Collapse of State Vector
10.8 Interpretation of Spin Measurement
10.9 Summary
11 The Feynman Path Integral
11.1 Probability Amplitude and Time Evolution
11.2 Evolution Kernel
11.3 Superposition of Trans-Empirical Paths
11.4 The Dirac–Feynman Formula
11.5 The Lagrangian
11.6 The Feynman Path Integral
11.7 Path Integral for Evolution Kernel
11.8 Composition Rule for Probability Amplitudes
11.9 Trans-Empirical Paths and Path Integral
11.10 State Vector and Trans-Empirical Paths
11.11 Path Integral Quantization: Action
11.12 Hamiltonian from Lagrangian
11.13 Summary
12 Conclusions
12.1 Three Formulations of Quantum Mechanics
12.2 Interpretations of Quantum Mechanics
Glossary of Terms
List of Symbols
References
Index