-
1 Introduction PostScript
or PDF
- 1.1 Scope of this Book
1.2 Quantum States and Variables
1.3 Quantum Dynamics
1.4 Mathematics I. Linear Algebra
1.5 Mathematics II. Calculus, Probability Theory
1.6 Quantum Reasoning
1.7 Quantum Measurements
1.8 Quantum Paradoxes
-
2 Wave Functions PostScript
or PDF
- 2.1 Classical and Quantum Particles
2.2 Physical Interpretation of the Wave Function
2.3 Wave Functions and Position
2.4 Wave Functions and Momentum
2.5 Toy Model
-
3 Linear Algebra In Dirac Notation
PostScript
or PDF
- 3.1 Hilbert Space and Inner Product
3.2 Linear Functionals and the Dual Space
3.3 Operators, Dyads
3.4 Projectors and Subspaces
3.5 Orthogonal Projectors and Orthonormal Bases
3.6 Column Vectors, Row Vectors, and Matrices
3.7 Diagonalization of Hermitian Operators
3.8 Trace
3.9 Positive Operators and Density Matrices
3.10 Functions of Operators
-
4 Physical Properties
PostScript
or PDF
- 4.1 Classical and Quantum Properties
4.2 Toy Model and Spin Half
4.3 Continuous Quantum Systems
4.4 Negation of Properties (NOT)
4.5 Conjunction and Disjunction (AND, OR)
4.6 Incompatible Properties
-
5 Probabilities and Physical Variables
PostScript
or PDF
- 5.1 Classical Sample Space and Event Algebra
5.2 Quantum Sample Space and Event Algebra
5.3 Refinement, Coarsening and Compatibility
5.4 Probabilities and Ensembles
5.5 Random Variables and Physical Variables
5.6 Averages
-
6 Composite Systems and Tensor Products
PostScript
or PDF
- 6.1 Introduction
6.2 Definition of tensor products
6.3 Examples of Composite Quantum Systems
6.4 Product Operators
6.5 General Operators, Matrix Elements, Partial Traces
6.6 Product Properties and Product of Sample Spaces
-
7 Unitary Dynamics
PostScript
or PDF
- 7.1 The Schrödinger Equation
7.2 Unitary Operators
7.3 Time Development Operators
7.4 Toy Models
-
8 Stochastic Histories
PostScript
or PDF
- 8.1 Introduction
8.2 Classical Histories
8.3 Quantum Histories
8.4 Extensions and Logical Operations on Histories
8.5 Sample Spaces and Families of Histories
8.6 Refinements of Histories
8.7 Unitary Histories
-
9 The Born Rule
PostScript
or PDF
- 9.1 Classical Random Walk
9.2 Single-Time Probabilities
9.3 The Born Rule
9.4 Wave Function as a Pre-Probability
9.5 Application: Alpha Decay
9.6 Schrödinger's Cat
-
10 Consistent Histories
PostScript
or PDF
- 10.1 Chain Operators and Weights
10.2 Consistency Conditions and Consistent Families
10.3 Examples of Consistent and Inconsistent Families
10.4 Refinement and Compatibility
-
11 Checking Consistency
PostScript
or PDF
- 11.1 Introduction
11.2 Support of a Consistent Family
11.3 Initial and Final Projectors
11.4 Heisenberg Representation
11.5 Fixed Initial State
11.6 Initial Pure State. Chain Kets
11.7 Unitary Extensions
11.8 Intrinsically Inconsistent Histories
-
12 Examples of Consistent Families
PostScript
or PDF
- 12.1 Toy Beam Splitter
12.2 Beam Splitter With Detector
12.3 Time-Elapse Detector
12.4 Toy Alpha Decay
-
13 Quantum Interference PostScript
or PDF
- 13.1 Two-Slit and Mach-Zehnder Interferometers
13.2 Toy Mach-Zehnder Interferometer
13.3 Detector in Output of Interferometer
13.4 Detector in Internal Arm of Interferometer
13.5 Weak Detectors in Internal Arms
-
14 Dependent (Contextual) Events PostScript
or PDF
- 14.1 An Example
14.2 Classical Analogy
14.3 Contextual Properties and Conditional Probabilities
14.4 Dependent Events in Histories
-
15 Density Matrices PostScript
or PDF
- 15.1 Introduction
15.2 Density Matrix as a Pre-Probability
15.3 Reduced Density Matrix for Subsystem
15.4 Time Dependence of Reduced Density Matrix
15.5 Reduced Density Matrix as Initial Condition
15.6 Density Matrix for Isolated System
15.7 Conditional Density Matrices
-
16 Quantum Reasoning PostScript
or PDF
- 16.1 Some General Principles
16.2 Example: Toy Beam Splitter
16.3 Internal Consistency of Quantum Reasoning
16.4 Interpretation of Multiple Frameworks
-
17 Measurements I PostScript
or PDF
- 17.1 Introduction
17.2 Microscopic Measurement
17.3 Macroscopic Measurement, First Version
17.4 Macroscopic Measurement, Second Version
17.5 General Destructive Measurements
-
18 Measurements II PostScript
or PDF
- 18.1 Beam Splitter and Successive Measurements
18.2 Wave Function Collapse
18.3 Nondestructive Stern-Gerlach Measurements
18.4 Measurements and Incompatible Families
18.5 General Nondestructive Measurements
-
19 Coins and Counterfactuals PostScript
or PDF
- 19.1 Quantum Paradoxes
19.2 Quantum Coins
19.3 Stochastic Counterfactuals
19.4 Quantum Counterfactuals
-
20 Delayed Choice Paradox PostScript
or PDF
- 20.1 Statement of the Paradox
20.2 Unitary Dynamics
20.3 Some Consistent Families
20.4 Quantum Coin Toss and Counterfactual Paradox
20.5 Conclusion
-
21 Indirect Measurement Paradox PostScript
or PDF
- 21.1 Statement of the Paradox
21.2 Unitary Dynamics
21.3 Comparing Min and Mout
21.4 Delayed Choice Version
21.5 Interaction-Free Measurement?
21.6 Conclusion
-
22 Incompatibility Paradoxes PostScript
or PDF
- 22.1 Simultaneous Values
22.2 Value Functionals
22.3 Paradox of Two Spins
22.4 Truth Functionals
22.5 Paradox of Three Boxes
22.6 Truth Functionals for Histories
-
23 Singlet State Correlations PostScript
or PDF
- 23.1 Introduction
23.2 Spin Correlations
23.3 Histories for Three Times
23.4 Measurements of One Spin
23.5 Measurements of Two Spins
-
24 EPR Paradox and Bell Inequalities PostScript
or PDF
- 24.1 Bohm Version of the EPR Paradox
24.2 Counterfactuals and the EPR Paradox
24.3 EPR and Hidden Variables
24.4 Bell Inequalities
-
25 Hardy's Paradox PostScript
or PDF
- 25.1 Introduction
25.2 The First Paradox
25.3 Analysis of the First Paradox
25.4 The Second Paradox
25.5 Analysis of the Second Paradox
-
26 Decoherence and the Classical Limit PostScript
or PDF
- 26.1 Introduction
26.2 Particle in an Interferometer
26.3 Density Matrix
26.4 Random Environment
26.5 Consistency of Histories
26.6 Decoherence and Classical Physics
-
27 Quantum Theory and Reality PostScript
or PDF
- 27.1 Introduction
27.2 Quantum vs. Classical Reality
27.3 Multiple Incompatible Descriptions
27.4 The Macroscopic World
27.5 Conclusion