Contents -- Preface -- Organisation -- Part 1 Preliminaries -- Chapter 1 Orientation and Outlook -- 1.1. General Orientation -- 1.2. Materialism -- 1.3. Materialism and Realism -- 1.4. Logic -- 1.5. Mathematics -- 1.6. Reversing Abstraction -- 1.7. Definitions, Laws of Nature and Causality -- 1.8. Foundations -- 1.9. Axioms -- 1.10. An Interpreted Theory -- Part 2 Probabilities -- Chapter 2 Simple Probabilities -- 2.1. Colloquial and Mathematical Terminology -- 2.2. Probabilities for Finite Systems -- 2.2.1. An Example: The Faces of a Cube -- 2.2.2. Dice: Statistical Methods of Measure -- 2.2.3. Loaded Dice: Statistical Methods of Measure -- 2.2.4. Standard Dice and Conservation Laws -- 2.3. Probability and Statistics -- 2.3.1. An Extreme Example -- 2.4. Probabilities in Deterministic Systems -- 2.5. The Referent of Probabilities and Measurement -- 2.5.1. Single System or Ensemble? -- 2.5.2. The Collapse of the Distribution -- 2.5.3. Hidden Variables -- 2.6. Preliminary Summary -- Chapter 3 A More Careful Look at Probabilities -- 3.1. Abstract Objects -- 3.2. States and Probability Distributions -- 3.2.1. The Propensity Interpretation -- 3.3. The Formal Definition of Probability -- 3.3.1. A Premonition -- 3.4. Time-Dependent Probabilities -- 3.5. Random Tests -- 3.6. Particle-Distribution Probabilities -- Part 3 Classical Mechanics -- Chapter 4 The Hamilton-Jacobi Equation -- 4.1. Historical Connections -- 4.2. The H-J Equation -- 4.3. Solutions of the H-J Equation -- 4.3.1. Cartesian Coordinates -- 4.3.2. Spherical Polar Coordinates -- 4.3.3. Comparisons -- 4.3.4. Cylindrical Coordinates -- 4.4. Distribution of Trajectories -- 4.5. Summary -- Appendix 4.A Transformation Theory -- Chapter 5 Angular Momentum -- 5.1. Coordinates and Momenta -- 5.2. The Angular Momentum "Vector".

5.3. The Poisson Brackets and Angular Momentum -- 5.4. Components of the Angular Momentum "Vector" -- 5.5. Conclusions for Angular Momentum -- Part 4 Schrödinger's Mechanics -- Chapter 6 Prelude: Particle Diffraction -- 6.1. History -- 6.1.1. The Experiment -- 6.1.2. The Explanations -- 6.2. The Wave Theory -- 6.3. The Particle Theory -- 6.4. A Simple Case -- 6.5. Experimental Verification -- 6.6. The Answer to a Rhetorical Question -- 6.7. Conclusion -- Chapter 7 The Genesis of Schrödinger's Mechanics -- 7.1. Lagrangians, Hamiltonians, Variation Principles -- 7.1.1. Equations and Identities -- 7.2. Replacing the Hamilton-Jacobi Equation -- 7.3. Generalising the Action S -- 7.3.1. Changing the Notation for Action -- 7.3.2. Interpreting the Change -- 7.4. Schrödinger's Dynamical Law -- 7.4.1. Position Probability and Energy Distributions -- 7.4.2. The Schrodinger Condition -- 7.5. Probability Distributions? -- 7.6. Summary of Basic Principles -- Chapter 8 The Schrödinger Equation -- 8.1. The Variational Derivation -- 8.2. Some Interpretation -- 8.3. The Boundary Conditions -- 8.4. The Time-Independent Schrödinger Equation -- Appendix 8.A Schrödinger's First Paper of 1926 -- Chapter 9 Identities: Momenta and Dynamical Variables -- 9.1. Momentum Definitions and Distributions -- 9.2. Abstract Particles of Constant Momentum -- 9.3. Action and Momenta in Schrödinger's Mechanics -- 9.4. Momenta and Kinetic Energy -- 9.5. Boundary Conditions -- 9.5.1. Constant Momenta and Kinetic Energy -- 9.5.2. Solution of the Schrodinger Equation -- 9.6. The "Particle in a Box" and Cyclic Boundary Conditions -- Chapter 10 Abstracting the Structure -- 10.1. The Idea of Mathematical Structure -- 10.1.1. A Pitfall of Abstraction: The Momentum Operator -- 10.2. States and Hilbert Space.

10.3. The Real Use of Abstract Structures -- Part 5 Interpretation from Applications -- Chapter 11 The Quantum Kepler Problem -- 11.1. Two Interacting Particles -- 11.2. Quantum Kepler Problem in a Plane -- 11.3. Abstract and Concrete Hydrogen Atoms -- 11.4. The Kepler Problem in Three Dimensions -- 11.5. The Separation of the Schrödinger Equation -- 11.6. Commuting Operators and Conservation -- 11.7. The Less Familiar Separations -- 11.7.1. The Everyday Solutions -- 11.8. Conservation in Concrete and Abstract Systems -- 11.9. Conclusions from the Kepler Problem -- 11.9.1. Concrete Objects and Symmetries -- Appendix 11.A Hamiltonians by Substitution? -- Chapter 12 The Harmonic Oscillator and Fields -- 12.1. The Schrödinger Equation for SHM -- 12.2. SHM Details -- 12.3. Factorisation Method -- 12.4. Interpreting the SHM Solutions -- 12.5. Vibrations of Fields and "Particles" -- 12.5.1. Phonons and Photons -- 12.6. Second Quantisation -- Chapter 13 Perturbation Theory and Epicycles -- 13.1. Perturbation Theories in General -- 13.2. Perturbed Schrödinger Equations -- 13.3. Polarisation of Electron Distribution -- 13.4. Interpretation of Perturbation Theory -- 13.5. Quantum Theory and Epicycles -- 13.6. Approximations to Non-existent Functions -- 13.7. Summary for Perturbation Theory -- Chapter 14 Formalisms and "Hidden" Variables -- 14.1. The Semi-empirical Method -- 14.2. The Chemical Bond -- 14.3. Dirac's Spin "Hamiltonian" -- 14.4. Interpretation of the Spin Hamiltonian -- Part 6 Disputes and Paradoxes -- Chapter 15 Measurement at the Microscopic Level -- 15.1. Recollection: Concrete and Abstract Objects -- 15.2. Statistical Estimates of Probabilities -- 15.2.1. von Neumann's Theory of Measurement -- 15.3. Measurement as "State Preparation" -- 15.4. Heisenberg's Uncertainty Principle.

15.4.1. Measurement and Decoherence -- 15.5. Measurement Generalities -- Appendix 15.A Standard Deviations of Conjugate Variables -- Chapter 16 Paradoxes -- 16.1. The Classical Limit -- 16.1.1. The Ehrenfest Relations -- 16.2. The Einstein-Podolsky-Rosen (EPR) Paradox -- 16.2.1. The EPR Original -- 16.2.2. Bohm's Modification -- 16.2.3. Bell's Inequality and Theorem -- 16.3. Bell's Assumptions -- 16.3.1. Lessons from EPR -- 16.3.2. Density of Spin and EPR -- 16.4. Zero-Point Energy -- Chapter 17 Beyond Schrödinger's Mechanics? -- 17.1. An Interregnum? -- 17.2. The Avant-Garde -- 17.3. The Break with the Past -- 17.4. Classical and Quantum Mechanics -- Index.