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Probability and Schrödinger's mechanics

Author: David B Cook
Publisher: River Edge, NJ : World Scientific, ©2002.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cook, David B. (David Branston).
Probability and Schrödinger's mechanics.
River Edge, NJ : World Scientific, ©2002
(DLC) 2002038054
(OCoLC)50948838
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David B Cook
ISBN: 9789812776402 9812776400 9789812381910 9812381910
OCLC Number: 285164550
Description: 1 online resource (xviii, 323 pages)
Contents: pt. 1. Preliminaries. ch. 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 --
pt. 2. Probabilities. ch. 2. Simple probabilities. 2.1. Colloquial and mathematical terminology. 2.2. Probabilities for finite systems. 2.3. Probability and statistics. 2.4. Probabilities in deterministic systems. 2.5. The referent of probabilities and measurement. 2.6. Preliminary summary --
ch. 3. A more careful look at probabilities. 3.1. Abstract objects. 3.2. States and probability distributions. 3.3. The formal definition of probability. 3.4. Time-dependent probabilities. 3.5. Random tests. 3.6. Particle-distribution probabilities --
pt. 3. Classical mechanics. ch. 4. The Hamilton-Jacobi equation. 4.1. Historical connections. 4.2. The H-J equation. 4.3. Solutions of the H-J equation. 4.4. Distribution of trajectories. 4.5. Summary --
ch. 5. Angular momentum. 5.1. Coordinates and momenta. 5.2. The angular momentum "vector". 5.3. The Poisson prackets and angular momentum. 5.4. Components of the angular momentum "vector". 5.5. Conclusions for angular momentum --
pt. 4. Schrödinger's mechanics. ch. 6. Prelude: particle diffraction. 6.1. History. 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 --
ch. 7. The genesis of Schrödinger's mechanics. 7.1. Lagrangians, Hamiltonians, variation principles. 7.2. Replacing the Hamilton-Jacobi equation. 7.3. Generalising the action S. 7.4. Schrödinger's dynamical law. 7.5. Probability distributions? 7.6. Summary of basic principles --
ch. 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 --
ch. 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. 9.6. The "particle in a box" and cyclic boundary conditions --
ch. 10. Abstracting the structure. 10.1. The idea of mathematical structure. 10.2. States and Hilbert space. 10.3. The real use of abstract structures. pt. 5. Interpretation from applications. ch. 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. 11.8. Conservation in concrete and abstract systems. 11.9. Conclusions from the Kepler problem --
ch. 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". 12.6. Second quantisation --
ch. 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 --
ch. 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 --
pt. 6. Disputes and paradoxes. ch. 15. Measurement at the microscopic level. 15.1. Recollection: concrete and abstract objects. 15.2. Statistical estimates of probabilities. 15.3. Measurement as "state preparation". 15.4. Heisenberg's uncertainty principle. 15.5. Measurement generalities --
ch. 16. Paradoxes. 16.1. The classical limit. 16.2. The Einstein-Podolsky-Rosen (EPR) paradox. 16.3. Bell's assumptions. 16.4. Zero-point energy --
ch. 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.
Responsibility: David B. Cook.

Abstract:

An examination of some of the problems of interpreting Schrodinger's mechanics. The outlook is materialist ("realist") and stresses the development of Schrodinger's mechanics from classical theories  Read more...

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