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040 MiAaPQ|beng|erda|epn|cMiAaPQ|dMiAaPQ
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
856 40 |uhttps://ebookcentral.proquest.com/lib/sinciatw/
detail.action?docID=1681681|zClick to View
