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Table of Contents
Intro
Preface
Contents
Acronyms
1 Waves and Particles
1.1 Overview
1.2 The Schrödinger Equation
1.3 Unitary Operators in Hilbert Space
1.3.1 Existence and Uniqueness of Solutions of the Schrödinger Equation
1.3.2 The Time Evolution Operators
1.3.3 Unitary Matrices and Rotations
1.3.4 Inner Product
1.3.5 Abstract Hilbert Space
1.4 Classical Mechanics
1.4.1 Definition of Newtonian Mechanics
1.4.2 Properties of Newtonian Mechanics
1.4.3 Hamiltonian Systems
1.5 The Double-Slit Experiment
1.5.1 Classical Predictions for Particles and Waves
1.5.2 Actual Outcome of the Experiment
1.5.3 Feynman's Discussion
1.6 Bohmian Mechanics
1.6.1 Definition of Bohmian Mechanics
1.6.2 Properties of Bohmian Mechanics
1.6.3 Historical Overview
1.6.4 Equivariance
1.6.5 The Double-Slit Experiment in Bohmian Mechanics
1.6.6 Delayed-Choice Experiments
Afshar's Experiment
Exercises
References
2 Some Observables
2.1 Fourier Transform and Momentum
2.1.1 Fourier Transform
2.1.2 Momentum
2.1.3 Momentum Operator
2.1.4 Tunnel Effect
2.1.5 External Magnetic Field
2.2 Operators and Observables
2.2.1 Heisenberg's Uncertainty Relation
2.2.2 Limitation to Knowledge
2.2.3 Self-Adjoint Operators
2.2.4 The Spectral Theorem
2.2.5 Born's Rule
2.2.6 Conservation Laws in Quantum Mechanics
2.2.7 The Dirac Delta Function
2.3 Spin
2.3.1 Spinors and Pauli Matrices
2.3.2 The Pauli Equation
2.3.3 The Stern-Gerlach Experiment
2.3.4 Bohmian Mechanics with Spin
2.3.5 Is an Electron a Spinning Ball?
2.3.6 Are There Actual Spin Values?
2.3.7 Many-Particle Systems
2.3.8 Representations of SO(3)
2.3.9 Inverted Stern-Gerlach Magnet and Contextuality
Exercises
3.3.4 Primitive Ontology
3.3.5 How GRW Theory Solves the Measurement Problem
3.3.6 Empirical Tests
3.3.7 The Need for a Primitive Ontology
3.4 The Copenhagen Interpretation
3.4.1 Two Realms
3.4.2 Elements of the Copenhagen View
Positivism
Purported Impossibility of Non-paradoxical Theories
Completeness of the Wave Function
Language of Measurement
Narratives, But No Serious Ones
3.4.3 Complementarity
3.4.4 Reactions to the Measurement Problem
3.4.5 The Transactional Interpretation
3.5 Many Worlds
3.5.1 Schrödinger's Many-Worlds Theory
Preface
Contents
Acronyms
1 Waves and Particles
1.1 Overview
1.2 The Schrödinger Equation
1.3 Unitary Operators in Hilbert Space
1.3.1 Existence and Uniqueness of Solutions of the Schrödinger Equation
1.3.2 The Time Evolution Operators
1.3.3 Unitary Matrices and Rotations
1.3.4 Inner Product
1.3.5 Abstract Hilbert Space
1.4 Classical Mechanics
1.4.1 Definition of Newtonian Mechanics
1.4.2 Properties of Newtonian Mechanics
1.4.3 Hamiltonian Systems
1.5 The Double-Slit Experiment
1.5.1 Classical Predictions for Particles and Waves
1.5.2 Actual Outcome of the Experiment
1.5.3 Feynman's Discussion
1.6 Bohmian Mechanics
1.6.1 Definition of Bohmian Mechanics
1.6.2 Properties of Bohmian Mechanics
1.6.3 Historical Overview
1.6.4 Equivariance
1.6.5 The Double-Slit Experiment in Bohmian Mechanics
1.6.6 Delayed-Choice Experiments
Afshar's Experiment
Exercises
References
2 Some Observables
2.1 Fourier Transform and Momentum
2.1.1 Fourier Transform
2.1.2 Momentum
2.1.3 Momentum Operator
2.1.4 Tunnel Effect
2.1.5 External Magnetic Field
2.2 Operators and Observables
2.2.1 Heisenberg's Uncertainty Relation
2.2.2 Limitation to Knowledge
2.2.3 Self-Adjoint Operators
2.2.4 The Spectral Theorem
2.2.5 Born's Rule
2.2.6 Conservation Laws in Quantum Mechanics
2.2.7 The Dirac Delta Function
2.3 Spin
2.3.1 Spinors and Pauli Matrices
2.3.2 The Pauli Equation
2.3.3 The Stern-Gerlach Experiment
2.3.4 Bohmian Mechanics with Spin
2.3.5 Is an Electron a Spinning Ball?
2.3.6 Are There Actual Spin Values?
2.3.7 Many-Particle Systems
2.3.8 Representations of SO(3)
2.3.9 Inverted Stern-Gerlach Magnet and Contextuality
Exercises
3.3.4 Primitive Ontology
3.3.5 How GRW Theory Solves the Measurement Problem
3.3.6 Empirical Tests
3.3.7 The Need for a Primitive Ontology
3.4 The Copenhagen Interpretation
3.4.1 Two Realms
3.4.2 Elements of the Copenhagen View
Positivism
Purported Impossibility of Non-paradoxical Theories
Completeness of the Wave Function
Language of Measurement
Narratives, But No Serious Ones
3.4.3 Complementarity
3.4.4 Reactions to the Measurement Problem
3.4.5 The Transactional Interpretation
3.5 Many Worlds
3.5.1 Schrödinger's Many-Worlds Theory