Probability and Schrödinger's mechanics /:
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 c...
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| Sprache: | English |
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World Scientific,
©2002.
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| Zusammenfassung: | 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. |
| Beschreibung: | 1 online resource (xviii, 323 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9789812776402 9812776400 |
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| 100 | 1 | |a Cook, David B. |q (David Branston) |1 https://id.oclc.org/worldcat/entity/E39PCjDKdjgHQtprm4pfFVjCFC |0 http://id.loc.gov/authorities/names/n87852423 | |
| 245 | 1 | 0 | |a Probability and Schrödinger's mechanics / |c David B. Cook. |
| 260 | |a River Edge, NJ : |b World Scientific, |c ©2002. | ||
| 300 | |a 1 online resource (xviii, 323 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Quantum theory. |0 http://id.loc.gov/authorities/subjects/sh85109469 | |
| 650 | 0 | |a Probabilities. |0 http://id.loc.gov/authorities/subjects/sh85107090 | |
| 650 | 2 | |a Quantum Theory |0 https://id.nlm.nih.gov/mesh/D011789 | |
| 650 | 2 | |a Probability |0 https://id.nlm.nih.gov/mesh/D011336 | |
| 650 | 6 | |a Théorie quantique. | |
| 650 | 6 | |a Probabilités. | |
| 650 | 7 | |a probability. |2 aat | |
| 650 | 7 | |a SCIENCE |x Physics |x Quantum Theory. |2 bisacsh | |
| 650 | 7 | |a Probabilities |2 fast | |
| 650 | 7 | |a Quantum theory |2 fast | |
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| author_GND | http://id.loc.gov/authorities/names/n87852423 |
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| 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. |
| ctrlnum | (OCoLC)285164550 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
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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.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">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.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Quantum theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85109469</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Probabilities.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85107090</subfield></datafield><datafield tag="650" ind1=" " ind2="2"><subfield code="a">Quantum Theory</subfield><subfield code="0">https://id.nlm.nih.gov/mesh/D011789</subfield></datafield><datafield tag="650" ind1=" " ind2="2"><subfield code="a">Probability</subfield><subfield code="0">https://id.nlm.nih.gov/mesh/D011336</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie quantique.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Probabilités.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">probability.</subfield><subfield code="2">aat</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Physics</subfield><subfield code="x">Quantum Theory.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Probabilities</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Quantum theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Probability and Schrödinger's mechanics (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCGdpqKh7rBFC76h6qW4dDC</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Cook, David B. 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| id | ZDB-4-EBA-ocn285164550 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:35Z |
| institution | BVB |
| isbn | 9789812776402 9812776400 |
| language | English |
| oclc_num | 285164550 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xviii, 323 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Cook, David B. (David Branston) https://id.oclc.org/worldcat/entity/E39PCjDKdjgHQtprm4pfFVjCFC http://id.loc.gov/authorities/names/n87852423 Probability and Schrödinger's mechanics / David B. Cook. River Edge, NJ : World Scientific, ©2002. 1 online resource (xviii, 323 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and index. Print version record. 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. 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. English. Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Probability https://id.nlm.nih.gov/mesh/D011336 Théorie quantique. Probabilités. probability. aat SCIENCE Physics Quantum Theory. bisacsh Probabilities fast Quantum theory fast has work: Probability and Schrödinger's mechanics (Text) https://id.oclc.org/worldcat/entity/E39PCGdpqKh7rBFC76h6qW4dDC https://id.oclc.org/worldcat/ontology/hasWork Print version: Cook, David B. (David Branston). Probability and Schrödinger's mechanics. River Edge, NJ : World Scientific, ©2002 9812381910 9789812381910 (DLC) 2002038054 (OCoLC)50948838 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210616 Volltext |
| spellingShingle | Cook, David B. (David Branston) Probability and Schrödinger's mechanics / 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. Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Probability https://id.nlm.nih.gov/mesh/D011336 Théorie quantique. Probabilités. probability. aat SCIENCE Physics Quantum Theory. bisacsh Probabilities fast Quantum theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85109469 http://id.loc.gov/authorities/subjects/sh85107090 https://id.nlm.nih.gov/mesh/D011789 https://id.nlm.nih.gov/mesh/D011336 |
| title | Probability and Schrödinger's mechanics / |
| title_auth | Probability and Schrödinger's mechanics / |
| title_exact_search | Probability and Schrödinger's mechanics / |
| title_full | Probability and Schrödinger's mechanics / David B. Cook. |
| title_fullStr | Probability and Schrödinger's mechanics / David B. Cook. |
| title_full_unstemmed | Probability and Schrödinger's mechanics / David B. Cook. |
| title_short | Probability and Schrödinger's mechanics / |
| title_sort | probability and schrodinger s mechanics |
| topic | Quantum theory. http://id.loc.gov/authorities/subjects/sh85109469 Probabilities. http://id.loc.gov/authorities/subjects/sh85107090 Quantum Theory https://id.nlm.nih.gov/mesh/D011789 Probability https://id.nlm.nih.gov/mesh/D011336 Théorie quantique. Probabilités. probability. aat SCIENCE Physics Quantum Theory. bisacsh Probabilities fast Quantum theory fast |
| topic_facet | Quantum theory. Probabilities. Quantum Theory Probability Théorie quantique. Probabilités. probability. SCIENCE Physics Quantum Theory. Probabilities Quantum theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210616 |
| work_keys_str_mv | AT cookdavidb probabilityandschrodingersmechanics |