The principles of Newtonian and quantum mechanics: the need for Planck's constant, h
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
c2001
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. [343]-351) and index 1. From Kepler to Schrödinger ... and beyond. 1.1. Classical mechanics -- 1.2. Symplectic mechanics -- 1.3. Action and Hamilton-Jacobi's theory -- 1.4. Quantum mechanics -- 1.5. The statistical interpretation of [symbol] -- 1.6. Quantum mechanics in phase space -- 1.7. Feynman's "Path integral" -- 1.8. Bohmian mechanics -- 1.9. Interpretations -- 2. Newtonian mechanics. 2.1. Maxwell's principle and the lagrange form -- 2.2. Hamilton's equations -- 2.3. Galilean covariance -- 2.4. Constants of the motion and integrable systems -- 2.5. Liouville's equation and statistical mechanics -- 3. THE symplectic group. 3.1. Symplectic matrices and Sp(n) -- 3.2. Symplectic invariance of Hamiitonian flows -- 3.3. The properties of Sp(n) -- 3.4. Quadratic Hamiltonians -- 3.5. The inhomogeneous symplectic group -- 3.6. An illuminating analogy -- 3.7. Gromov's non-squeezing theorem -- 3.8. Symplectic capacity and periodic orbits -- 3.9. Capacity and periodic orbits -- - 3.10. Cell quantization of phase space -- 4. Action and phase. 4.1. Introduction -- 4.2. The fundamental property of the Poincaré-Cartan form -- 4.3. Free symplectomorphisms and generating functions -- 4.4. Generating functions and action -- 4.5. Short-time approximations to the action -- 4.6. Lagrangian manifolds -- 4.7. The phase of a Lagrangian manifold -- 4.8. Keller-Maslov quantization -- 5. Semi-classical mechanics. 5.1. Bohmian motion and half-densities -- 5.2. The Leray index and the signature function -- 5.3. De Rham forms -- 5.4. Wave-forms on a Lagrangian manifold -- 6. The metaplectic group and the Maslov index. 6.1. Introduction -- 6.2. Free symplectic matrices and their generating functions -- 6.3. The metaplectic group Mp(n) -- 6.4. The projections II and II[symbol] -- 6.5. The Maslov index on Mp(n) -- 6.6. The cohomological meaning of the Maslov index -- 6.7. The inhomogeneous metaplectic group -- 6.8. The metaplectic group and wave optics -- - 6.9. The groups Symp(n) and Ham(n) -- 7. Schrödinger 's equation and the metatron. 7.1. Schrödinger 's equation for the free particle -- 7.2. Van Vleck's determinant -- 7.3. The continuity equation for Van Vleck's density -- 7.4. The short-time propagator -- 7.5. The case of quadratic Hamiltonians -- 7.6. Solving Schrödinger 's equation: general case -- 7.7. Metatrons and the implicate order -- 7.8. Phase space and Schrödinger 's equation This book deals with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the "principle of the symplectic camel", which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introduced, in connection with the Bohmian theory of motion. A precise form of Feynman's integral is introduced in connection with the extended metaplectic representation |
| Beschreibung: | 1 Online-Ressource (xxii, 357 p.) |
| ISBN: | 1848161425 1860942741 9781848161429 9781860942747 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV043152766 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151126s2001 |||| o||u| ||||||eng d | ||
| 020 | |a 1848161425 |c electronic bk. |9 1-84816-142-5 | ||
| 020 | |a 1860942741 |c alk. paper |9 1-86094-274-1 | ||
| 020 | |a 9781848161429 |c electronic bk. |9 978-1-84816-142-9 | ||
| 020 | |a 9781860942747 |9 978-1-86094-274-7 | ||
| 035 | |a (OCoLC)646768357 | ||
| 035 | |a (DE-599)BVBBV043152766 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1047 | ||
| 082 | 0 | |a 530.15/564 |2 22 | |
| 100 | 1 | |a Gosson, Maurice de |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The principles of Newtonian and quantum mechanics |b the need for Planck's constant, h |c M A de Gosson |
| 264 | 1 | |a London |b Imperial College Press |c c2001 | |
| 300 | |a 1 Online-Ressource (xxii, 357 p.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 500 | |a Includes bibliographical references (p. [343]-351) and index | ||
| 500 | |a 1. From Kepler to Schrödinger ... and beyond. 1.1. Classical mechanics -- 1.2. Symplectic mechanics -- 1.3. Action and Hamilton-Jacobi's theory -- 1.4. Quantum mechanics -- 1.5. The statistical interpretation of [symbol] -- 1.6. Quantum mechanics in phase space -- 1.7. Feynman's "Path integral" -- 1.8. Bohmian mechanics -- 1.9. Interpretations -- 2. Newtonian mechanics. 2.1. Maxwell's principle and the lagrange form -- 2.2. Hamilton's equations -- 2.3. Galilean covariance -- 2.4. Constants of the motion and integrable systems -- 2.5. Liouville's equation and statistical mechanics -- 3. THE symplectic group. 3.1. Symplectic matrices and Sp(n) -- 3.2. Symplectic invariance of Hamiitonian flows -- 3.3. The properties of Sp(n) -- 3.4. Quadratic Hamiltonians -- 3.5. The inhomogeneous symplectic group -- 3.6. An illuminating analogy -- 3.7. Gromov's non-squeezing theorem -- 3.8. Symplectic capacity and periodic orbits -- 3.9. Capacity and periodic orbits -- | ||
| 500 | |a - 3.10. Cell quantization of phase space -- 4. Action and phase. 4.1. Introduction -- 4.2. The fundamental property of the Poincaré-Cartan form -- 4.3. Free symplectomorphisms and generating functions -- 4.4. Generating functions and action -- 4.5. Short-time approximations to the action -- 4.6. Lagrangian manifolds -- 4.7. The phase of a Lagrangian manifold -- 4.8. Keller-Maslov quantization -- 5. Semi-classical mechanics. 5.1. Bohmian motion and half-densities -- 5.2. The Leray index and the signature function -- 5.3. De Rham forms -- 5.4. Wave-forms on a Lagrangian manifold -- 6. The metaplectic group and the Maslov index. 6.1. Introduction -- 6.2. Free symplectic matrices and their generating functions -- 6.3. The metaplectic group Mp(n) -- 6.4. The projections II and II[symbol] -- 6.5. The Maslov index on Mp(n) -- 6.6. The cohomological meaning of the Maslov index -- 6.7. The inhomogeneous metaplectic group -- 6.8. The metaplectic group and wave optics -- | ||
| 500 | |a - 6.9. The groups Symp(n) and Ham(n) -- 7. Schrödinger 's equation and the metatron. 7.1. Schrödinger 's equation for the free particle -- 7.2. Van Vleck's determinant -- 7.3. The continuity equation for Van Vleck's density -- 7.4. The short-time propagator -- 7.5. The case of quadratic Hamiltonians -- 7.6. Solving Schrödinger 's equation: general case -- 7.7. Metatrons and the implicate order -- 7.8. Phase space and Schrödinger 's equation | ||
| 500 | |a This book deals with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the "principle of the symplectic camel", which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introduced, in connection with the Bohmian theory of motion. A precise form of Feynman's integral is introduced in connection with the extended metaplectic representation | ||
| 650 | 7 | |a SCIENCE / Physics / Mathematical & Computational |2 bisacsh | |
| 650 | 7 | |a Geometric quantization |2 fast | |
| 650 | 7 | |a Lagrangian functions |2 fast | |
| 650 | 7 | |a Maslov index |2 fast | |
| 650 | 4 | |a Lagrangian functions | |
| 650 | 4 | |a Maslov index | |
| 650 | 4 | |a Geometric quantization | |
| 650 | 0 | 7 | |a Symplektische Geometrie |0 (DE-588)4194232-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Maslov-Index |0 (DE-588)4169023-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrische Quantisierung |0 (DE-588)4156720-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mechanik |0 (DE-588)4038168-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenmechanik |0 (DE-588)4047989-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Physik |0 (DE-588)4037952-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lagrange-Funktion |0 (DE-588)4166459-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mechanik |0 (DE-588)4038168-7 |D s |
| 689 | 0 | 1 | |a Quantenmechanik |0 (DE-588)4047989-4 |D s |
| 689 | 0 | 2 | |a Mathematische Physik |0 (DE-588)4037952-8 |D s |
| 689 | 0 | 3 | |a Symplektische Geometrie |0 (DE-588)4194232-2 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 689 | 1 | 0 | |a Lagrange-Funktion |0 (DE-588)4166459-0 |D s |
| 689 | 1 | 1 | |a Maslov-Index |0 (DE-588)4169023-0 |D s |
| 689 | 1 | 2 | |a Geometrische Quantisierung |0 (DE-588)4156720-1 |D s |
| 689 | 1 | |8 2\p |5 DE-604 | |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235535 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028576957 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235535 |l FAW01 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235535 |l FAW02 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804175614571184128 |
|---|---|
| any_adam_object | |
| author | Gosson, Maurice de |
| author_facet | Gosson, Maurice de |
| author_role | aut |
| author_sort | Gosson, Maurice de |
| author_variant | m d g md mdg |
| building | Verbundindex |
| bvnumber | BV043152766 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)646768357 (DE-599)BVBBV043152766 |
| dewey-full | 530.15/564 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15/564 |
| dewey-search | 530.15/564 |
| dewey-sort | 3530.15 3564 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06190nmm a2200709zc 4500</leader><controlfield tag="001">BV043152766</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151126s2001 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1848161425</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">1-84816-142-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1860942741</subfield><subfield code="c">alk. paper</subfield><subfield code="9">1-86094-274-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781848161429</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-1-84816-142-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781860942747</subfield><subfield code="9">978-1-86094-274-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)646768357</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043152766</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.15/564</subfield><subfield code="2">22</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gosson, Maurice de</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The principles of Newtonian and quantum mechanics</subfield><subfield code="b">the need for Planck's constant, h</subfield><subfield code="c">M A de Gosson</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London</subfield><subfield code="b">Imperial College Press</subfield><subfield code="c">c2001</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (xxii, 357 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (p. [343]-351) and index</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">1. From Kepler to Schrödinger ... and beyond. 1.1. Classical mechanics -- 1.2. Symplectic mechanics -- 1.3. Action and Hamilton-Jacobi's theory -- 1.4. Quantum mechanics -- 1.5. The statistical interpretation of [symbol] -- 1.6. Quantum mechanics in phase space -- 1.7. Feynman's "Path integral" -- 1.8. Bohmian mechanics -- 1.9. Interpretations -- 2. Newtonian mechanics. 2.1. Maxwell's principle and the lagrange form -- 2.2. Hamilton's equations -- 2.3. Galilean covariance -- 2.4. Constants of the motion and integrable systems -- 2.5. Liouville's equation and statistical mechanics -- 3. THE symplectic group. 3.1. Symplectic matrices and Sp(n) -- 3.2. Symplectic invariance of Hamiitonian flows -- 3.3. The properties of Sp(n) -- 3.4. Quadratic Hamiltonians -- 3.5. The inhomogeneous symplectic group -- 3.6. An illuminating analogy -- 3.7. Gromov's non-squeezing theorem -- 3.8. Symplectic capacity and periodic orbits -- 3.9. Capacity and periodic orbits -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 3.10. Cell quantization of phase space -- 4. Action and phase. 4.1. Introduction -- 4.2. The fundamental property of the Poincaré-Cartan form -- 4.3. Free symplectomorphisms and generating functions -- 4.4. Generating functions and action -- 4.5. Short-time approximations to the action -- 4.6. Lagrangian manifolds -- 4.7. The phase of a Lagrangian manifold -- 4.8. Keller-Maslov quantization -- 5. Semi-classical mechanics. 5.1. Bohmian motion and half-densities -- 5.2. The Leray index and the signature function -- 5.3. De Rham forms -- 5.4. Wave-forms on a Lagrangian manifold -- 6. The metaplectic group and the Maslov index. 6.1. Introduction -- 6.2. Free symplectic matrices and their generating functions -- 6.3. The metaplectic group Mp(n) -- 6.4. The projections II and II[symbol] -- 6.5. The Maslov index on Mp(n) -- 6.6. The cohomological meaning of the Maslov index -- 6.7. The inhomogeneous metaplectic group -- 6.8. The metaplectic group and wave optics -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 6.9. The groups Symp(n) and Ham(n) -- 7. Schrödinger 's equation and the metatron. 7.1. Schrödinger 's equation for the free particle -- 7.2. Van Vleck's determinant -- 7.3. The continuity equation for Van Vleck's density -- 7.4. The short-time propagator -- 7.5. The case of quadratic Hamiltonians -- 7.6. Solving Schrödinger 's equation: general case -- 7.7. Metatrons and the implicate order -- 7.8. Phase space and Schrödinger 's equation</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book deals with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the "principle of the symplectic camel", which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introduced, in connection with the Bohmian theory of motion. A precise form of Feynman's integral is introduced in connection with the extended metaplectic representation</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE / Physics / Mathematical & Computational</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometric quantization</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Lagrangian functions</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Maslov index</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lagrangian functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Maslov index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometric quantization</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Symplektische Geometrie</subfield><subfield code="0">(DE-588)4194232-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Maslov-Index</subfield><subfield code="0">(DE-588)4169023-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Geometrische Quantisierung</subfield><subfield code="0">(DE-588)4156720-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mechanik</subfield><subfield code="0">(DE-588)4038168-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Quantenmechanik</subfield><subfield code="0">(DE-588)4047989-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Lagrange-Funktion</subfield><subfield code="0">(DE-588)4166459-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mechanik</subfield><subfield code="0">(DE-588)4038168-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Quantenmechanik</subfield><subfield code="0">(DE-588)4047989-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Mathematische Physik</subfield><subfield code="0">(DE-588)4037952-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="3"><subfield code="a">Symplektische Geometrie</subfield><subfield code="0">(DE-588)4194232-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Lagrange-Funktion</subfield><subfield code="0">(DE-588)4166459-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Maslov-Index</subfield><subfield code="0">(DE-588)4169023-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="2"><subfield code="a">Geometrische Quantisierung</subfield><subfield code="0">(DE-588)4156720-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235535</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028576957</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235535</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235535</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV043152766 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:05Z |
| institution | BVB |
| isbn | 1848161425 1860942741 9781848161429 9781860942747 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028576957 |
| oclc_num | 646768357 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xxii, 357 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Gosson, Maurice de Verfasser aut The principles of Newtonian and quantum mechanics the need for Planck's constant, h M A de Gosson London Imperial College Press c2001 1 Online-Ressource (xxii, 357 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. [343]-351) and index 1. From Kepler to Schrödinger ... and beyond. 1.1. Classical mechanics -- 1.2. Symplectic mechanics -- 1.3. Action and Hamilton-Jacobi's theory -- 1.4. Quantum mechanics -- 1.5. The statistical interpretation of [symbol] -- 1.6. Quantum mechanics in phase space -- 1.7. Feynman's "Path integral" -- 1.8. Bohmian mechanics -- 1.9. Interpretations -- 2. Newtonian mechanics. 2.1. Maxwell's principle and the lagrange form -- 2.2. Hamilton's equations -- 2.3. Galilean covariance -- 2.4. Constants of the motion and integrable systems -- 2.5. Liouville's equation and statistical mechanics -- 3. THE symplectic group. 3.1. Symplectic matrices and Sp(n) -- 3.2. Symplectic invariance of Hamiitonian flows -- 3.3. The properties of Sp(n) -- 3.4. Quadratic Hamiltonians -- 3.5. The inhomogeneous symplectic group -- 3.6. An illuminating analogy -- 3.7. Gromov's non-squeezing theorem -- 3.8. Symplectic capacity and periodic orbits -- 3.9. Capacity and periodic orbits -- - 3.10. Cell quantization of phase space -- 4. Action and phase. 4.1. Introduction -- 4.2. The fundamental property of the Poincaré-Cartan form -- 4.3. Free symplectomorphisms and generating functions -- 4.4. Generating functions and action -- 4.5. Short-time approximations to the action -- 4.6. Lagrangian manifolds -- 4.7. The phase of a Lagrangian manifold -- 4.8. Keller-Maslov quantization -- 5. Semi-classical mechanics. 5.1. Bohmian motion and half-densities -- 5.2. The Leray index and the signature function -- 5.3. De Rham forms -- 5.4. Wave-forms on a Lagrangian manifold -- 6. The metaplectic group and the Maslov index. 6.1. Introduction -- 6.2. Free symplectic matrices and their generating functions -- 6.3. The metaplectic group Mp(n) -- 6.4. The projections II and II[symbol] -- 6.5. The Maslov index on Mp(n) -- 6.6. The cohomological meaning of the Maslov index -- 6.7. The inhomogeneous metaplectic group -- 6.8. The metaplectic group and wave optics -- - 6.9. The groups Symp(n) and Ham(n) -- 7. Schrödinger 's equation and the metatron. 7.1. Schrödinger 's equation for the free particle -- 7.2. Van Vleck's determinant -- 7.3. The continuity equation for Van Vleck's density -- 7.4. The short-time propagator -- 7.5. The case of quadratic Hamiltonians -- 7.6. Solving Schrödinger 's equation: general case -- 7.7. Metatrons and the implicate order -- 7.8. Phase space and Schrödinger 's equation This book deals with the foundations of classical physics from the "symplectic" point of view, and of quantum mechanics from the "metaplectic" point of view. The Bohmian interpretation of quantum mechanics is discussed. Phase space quantization is achieved using the "principle of the symplectic camel", which is a recently discovered deep topological property of Hamiltonian flows. The mathematical tools developed in this book are the theory of the metaplectic group, the Maslov index in a precise form, and the Leray index of a pair of Lagrangian planes. The concept of the "metatron" is introduced, in connection with the Bohmian theory of motion. A precise form of Feynman's integral is introduced in connection with the extended metaplectic representation SCIENCE / Physics / Mathematical & Computational bisacsh Geometric quantization fast Lagrangian functions fast Maslov index fast Lagrangian functions Maslov index Geometric quantization Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Maslov-Index (DE-588)4169023-0 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Lagrange-Funktion (DE-588)4166459-0 gnd rswk-swf Mechanik (DE-588)4038168-7 s Quantenmechanik (DE-588)4047989-4 s Mathematische Physik (DE-588)4037952-8 s Symplektische Geometrie (DE-588)4194232-2 s 1\p DE-604 Lagrange-Funktion (DE-588)4166459-0 s Maslov-Index (DE-588)4169023-0 s Geometrische Quantisierung (DE-588)4156720-1 s 2\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235535 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gosson, Maurice de The principles of Newtonian and quantum mechanics the need for Planck's constant, h SCIENCE / Physics / Mathematical & Computational bisacsh Geometric quantization fast Lagrangian functions fast Maslov index fast Lagrangian functions Maslov index Geometric quantization Symplektische Geometrie (DE-588)4194232-2 gnd Maslov-Index (DE-588)4169023-0 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd Mechanik (DE-588)4038168-7 gnd Quantenmechanik (DE-588)4047989-4 gnd Mathematische Physik (DE-588)4037952-8 gnd Lagrange-Funktion (DE-588)4166459-0 gnd |
| subject_GND | (DE-588)4194232-2 (DE-588)4169023-0 (DE-588)4156720-1 (DE-588)4038168-7 (DE-588)4047989-4 (DE-588)4037952-8 (DE-588)4166459-0 |
| title | The principles of Newtonian and quantum mechanics the need for Planck's constant, h |
| title_auth | The principles of Newtonian and quantum mechanics the need for Planck's constant, h |
| title_exact_search | The principles of Newtonian and quantum mechanics the need for Planck's constant, h |
| title_full | The principles of Newtonian and quantum mechanics the need for Planck's constant, h M A de Gosson |
| title_fullStr | The principles of Newtonian and quantum mechanics the need for Planck's constant, h M A de Gosson |
| title_full_unstemmed | The principles of Newtonian and quantum mechanics the need for Planck's constant, h M A de Gosson |
| title_short | The principles of Newtonian and quantum mechanics |
| title_sort | the principles of newtonian and quantum mechanics the need for planck s constant h |
| title_sub | the need for Planck's constant, h |
| topic | SCIENCE / Physics / Mathematical & Computational bisacsh Geometric quantization fast Lagrangian functions fast Maslov index fast Lagrangian functions Maslov index Geometric quantization Symplektische Geometrie (DE-588)4194232-2 gnd Maslov-Index (DE-588)4169023-0 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd Mechanik (DE-588)4038168-7 gnd Quantenmechanik (DE-588)4047989-4 gnd Mathematische Physik (DE-588)4037952-8 gnd Lagrange-Funktion (DE-588)4166459-0 gnd |
| topic_facet | SCIENCE / Physics / Mathematical & Computational Geometric quantization Lagrangian functions Maslov index Symplektische Geometrie Maslov-Index Geometrische Quantisierung Mechanik Quantenmechanik Mathematische Physik Lagrange-Funktion |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=235535 |
| work_keys_str_mv | AT gossonmauricede theprinciplesofnewtonianandquantummechanicstheneedforplancksconstanth |