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050  4 QC174.17.P45C66 2002 
082 0  530.12 
100 1  Cook, David B 
245 10 Probability And Schrodinger's Mechanics 
264  1 Singapore :|bWorld Scientific Publishing Company,|c2002 
264  4 |c©2002 
300    1 online resource (343 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
505 0  Intro -- 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 
505 8  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 
505 8  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 
505 8  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 
520    This book addresses some of the problems of interpreting 
       Schrödinger's mechanics - the most complete and explicit 
       theory falling under the umbrella of "quantum theory". The
       outlook is materialist ("realist") and stresses the 
       development of Schrödinger's mechanics from classical 
       theories and its close connections with (particularly) the
       Hamilton-Jacobi theory. Emphasis is placed on the concepts
       and use of the modern objective (measure-theoretic) 
       probability theory. The work is free from any mention of 
       the bearing of Schrödinger's mechanics on God, his alleged
       mind or, indeed, minds at all. The author has taken the 
       naïve view that this mechanics is about the structure and 
       dynamics of atomic and sub-atomic systems since he has 
       been unable to trace any references to minds, 
       consciousness or measurements in the foundations of the 
       theory. Contents: Preliminaries: Orientation and Outlook; 
       Probabilities: Simple Probabilities; A More Careful Look 
       at Probabilities; Classical Mechanics: The Hamilton-Jacobi
       Equation; Angular Momentum; Schrödinger's Mechanics: 
       Prelude: Particle Diffraction; The Genesis of 
       Schrödinger's Mechanics; The Schrödinger Equation; 
       Identities: Momenta and Dynamical Variables; Abstracting 
       the Structure; Interpretation from Applications: The 
       Quantum Kepler Problem; The Harmonic Oscillator and 
       Fields; Perturbation Theory and Epicycles; Formalisms and 
       "Hidden" Variables; Disputes and Paradoxes: Measurement at
       the Microscopic Level; Paradoxes; Beyond Schrödinger's 
       Mechanics?. Readership: Physical scientists interested in 
       quantum theory, philosophers of science, and students of 
       scientific philosophy 
588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
       may be limited to ProQuest Ebook Central affiliated 
       libraries 
650  0 Quantum theory.;Probabilities 
655  4 Electronic books 
700 1  Leong, H.T 
700 1  Doyle, Anthony 
776 08 |iPrint version:|aCook, David B|tProbability And 
       Schrodinger's Mechanics|dSingapore : World Scientific 
       Publishing Company,c2002|z9789812381910 
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