The principles of Newtonian and quantum mechanics :: the need for Planck's constant, h /
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 "princip...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London : River Edge, NJ :
Imperial College Press ; Distributed by World Scientific Pub.,
©2001.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 resource (xxii, 357 pages) |
| Bibliographie: | Includes bibliographical references (pages 343-351) and index. |
| ISBN: | 9781848161429 1848161425 1281865982 9781281865984 9786611865986 6611865985 |
Internformat
MARC
| LEADER | 00000cam a2200000Ma 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn646768357 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cn||||||||| | ||
| 008 | 010404s2001 enk ob 001 0 eng d | ||
| 010 | |z 2001024570 | ||
| 040 | |a E7B |b eng |e pn |c E7B |d OCLCQ |d N$T |d IDEBK |d OCLCQ |d OCLCF |d I9W |d NLGGC |d YDXCP |d OCLCQ |d AZK |d LOA |d COCUF |d AGLDB |d CCO |d PIFAG |d VGM |d OCLCQ |d WRM |d OCLCQ |d VTS |d NRAMU |d VT2 |d OCLCQ |d WYU |d STF |d LEAUB |d UKAHL |d OCLCO |d QGK |d OCLCQ |d OCLCO |d SXB |d OCLCQ | ||
| 019 | |a 261122883 |a 642298159 |a 764499555 |a 961537172 |a 962678640 |a 1259240562 | ||
| 020 | |a 9781848161429 |q (electronic bk.) | ||
| 020 | |a 1848161425 |q (electronic bk.) | ||
| 020 | |z 9781860942747 | ||
| 020 | |z 1860942741 |q (alk. paper) | ||
| 020 | |a 1281865982 | ||
| 020 | |a 9781281865984 | ||
| 020 | |a 9786611865986 | ||
| 020 | |a 6611865985 | ||
| 035 | |a (OCoLC)646768357 |z (OCoLC)261122883 |z (OCoLC)642298159 |z (OCoLC)764499555 |z (OCoLC)961537172 |z (OCoLC)962678640 |z (OCoLC)1259240562 | ||
| 050 | 4 | |a QC20.7.C3 |b G67 2001eb | |
| 072 | 7 | |a SCI |x 040000 |2 bisacsh | |
| 082 | 7 | |a 530.15/564 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Gosson, Maurice de. | |
| 245 | 1 | 4 | |a The principles of Newtonian and quantum mechanics : |b the need for Planck's constant, h / |c M A de Gosson. |
| 260 | |a London : |b Imperial College Press ; |a River Edge, NJ : |b Distributed by World Scientific Pub., |c ©2001. | ||
| 300 | |a 1 online resource (xxii, 357 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 (pages 343-351) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |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 -- 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. | |
| 520 | |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. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Lagrangian functions. |0 http://id.loc.gov/authorities/subjects/sh85073965 | |
| 650 | 0 | |a Maslov index. |0 http://id.loc.gov/authorities/subjects/sh85081825 | |
| 650 | 0 | |a Geometric quantization. |0 http://id.loc.gov/authorities/subjects/sh85054127 | |
| 650 | 6 | |a Fonctions de Lagrange. | |
| 650 | 6 | |a Indices de Maslov. | |
| 650 | 6 | |a Quantification géométrique. | |
| 650 | 7 | |a SCIENCE |x Physics |x 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 | 7 | |a Maslov, Índex de. |2 lemac | |
| 776 | 0 | 8 | |i Print version: |a Gosson, Maurice de. |t Principles of Newtonian and quantum mechanics. |d London : Imperial College Press ; River Edge, NJ : Distributed by World Scientific Pub., ©2001 |w (DLC) 2001024570 |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235535 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH24682555 | ||
| 938 | |a ebrary |b EBRY |n ebr10255544 | ||
| 938 | |a EBSCOhost |b EBSC |n 235535 | ||
| 938 | |a YBP Library Services |b YANK |n 2889011 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn646768357 |
|---|---|
| _version_ | 1816881725128572928 |
| adam_text | |
| any_adam_object | |
| author | Gosson, Maurice de |
| author_facet | Gosson, Maurice de |
| author_role | |
| author_sort | Gosson, Maurice de |
| author_variant | m d g md mdg |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.C3 G67 2001eb |
| callnumber-search | QC20.7.C3 G67 2001eb |
| callnumber-sort | QC 220.7 C3 G67 42001EB |
| callnumber-subject | QC - Physics |
| collection | ZDB-4-EBA |
| contents | 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. |
| ctrlnum | (OCoLC)646768357 |
| 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>06052cam a2200649Ma 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn646768357</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cn|||||||||</controlfield><controlfield tag="008">010404s2001 enk ob 001 0 eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="z"> 2001024570</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">E7B</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">E7B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">N$T</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">I9W</subfield><subfield code="d">NLGGC</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AZK</subfield><subfield code="d">LOA</subfield><subfield code="d">COCUF</subfield><subfield code="d">AGLDB</subfield><subfield code="d">CCO</subfield><subfield code="d">PIFAG</subfield><subfield code="d">VGM</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WRM</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">NRAMU</subfield><subfield code="d">VT2</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">STF</subfield><subfield code="d">LEAUB</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCO</subfield><subfield code="d">QGK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">SXB</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">261122883</subfield><subfield code="a">642298159</subfield><subfield code="a">764499555</subfield><subfield code="a">961537172</subfield><subfield code="a">962678640</subfield><subfield code="a">1259240562</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781848161429</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1848161425</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9781860942747</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">1860942741</subfield><subfield code="q">(alk. paper)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1281865982</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781281865984</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9786611865986</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">6611865985</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)646768357</subfield><subfield code="z">(OCoLC)261122883</subfield><subfield code="z">(OCoLC)642298159</subfield><subfield code="z">(OCoLC)764499555</subfield><subfield code="z">(OCoLC)961537172</subfield><subfield code="z">(OCoLC)962678640</subfield><subfield code="z">(OCoLC)1259240562</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QC20.7.C3</subfield><subfield code="b">G67 2001eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">SCI</subfield><subfield code="x">040000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">530.15/564</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gosson, Maurice de.</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><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="260" ind1=" " ind2=" "><subfield code="a">London :</subfield><subfield code="b">Imperial College Press ;</subfield><subfield code="a">River Edge, NJ :</subfield><subfield code="b">Distributed by World Scientific Pub.,</subfield><subfield code="c">©2001.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xxii, 357 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 343-351) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" 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 -- 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.</subfield></datafield><datafield tag="520" 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="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Lagrangian functions.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85073965</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Maslov index.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85081825</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Geometric quantization.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85054127</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Fonctions de Lagrange.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Indices de Maslov.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Quantification géométrique.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Physics</subfield><subfield code="x">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="7"><subfield code="a">Maslov, Índex de.</subfield><subfield code="2">lemac</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Gosson, Maurice de.</subfield><subfield code="t">Principles of Newtonian and quantum mechanics.</subfield><subfield code="d">London : Imperial College Press ; River Edge, NJ : Distributed by World Scientific Pub., ©2001</subfield><subfield code="w">(DLC) 2001024570</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235535</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24682555</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10255544</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">235535</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2889011</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn646768357 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:17:17Z |
| institution | BVB |
| isbn | 9781848161429 1848161425 1281865982 9781281865984 9786611865986 6611865985 |
| language | English |
| oclc_num | 646768357 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxii, 357 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Imperial College Press ; Distributed by World Scientific Pub., |
| record_format | marc |
| spelling | Gosson, Maurice de. The principles of Newtonian and quantum mechanics : the need for Planck's constant, h / M A de Gosson. London : Imperial College Press ; River Edge, NJ : Distributed by World Scientific Pub., ©2001. 1 online resource (xxii, 357 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 343-351) and index. Print version record. 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. English. Lagrangian functions. http://id.loc.gov/authorities/subjects/sh85073965 Maslov index. http://id.loc.gov/authorities/subjects/sh85081825 Geometric quantization. http://id.loc.gov/authorities/subjects/sh85054127 Fonctions de Lagrange. Indices de Maslov. Quantification géométrique. SCIENCE Physics Mathematical & Computational. bisacsh Geometric quantization fast Lagrangian functions fast Maslov index fast Maslov, Índex de. lemac Print version: Gosson, Maurice de. Principles of Newtonian and quantum mechanics. London : Imperial College Press ; River Edge, NJ : Distributed by World Scientific Pub., ©2001 (DLC) 2001024570 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235535 Volltext |
| spellingShingle | Gosson, Maurice de The principles of Newtonian and quantum mechanics : the need for Planck's constant, h / 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. Lagrangian functions. http://id.loc.gov/authorities/subjects/sh85073965 Maslov index. http://id.loc.gov/authorities/subjects/sh85081825 Geometric quantization. http://id.loc.gov/authorities/subjects/sh85054127 Fonctions de Lagrange. Indices de Maslov. Quantification géométrique. SCIENCE Physics Mathematical & Computational. bisacsh Geometric quantization fast Lagrangian functions fast Maslov index fast Maslov, Índex de. lemac |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85073965 http://id.loc.gov/authorities/subjects/sh85081825 http://id.loc.gov/authorities/subjects/sh85054127 |
| 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 | principles of newtonian and quantum mechanics the need for planck s constant h |
| title_sub | the need for Planck's constant, h / |
| topic | Lagrangian functions. http://id.loc.gov/authorities/subjects/sh85073965 Maslov index. http://id.loc.gov/authorities/subjects/sh85081825 Geometric quantization. http://id.loc.gov/authorities/subjects/sh85054127 Fonctions de Lagrange. Indices de Maslov. Quantification géométrique. SCIENCE Physics Mathematical & Computational. bisacsh Geometric quantization fast Lagrangian functions fast Maslov index fast Maslov, Índex de. lemac |
| topic_facet | Lagrangian functions. Maslov index. Geometric quantization. Fonctions de Lagrange. Indices de Maslov. Quantification géométrique. SCIENCE Physics Mathematical & Computational. Geometric quantization Lagrangian functions Maslov index Maslov, Índex de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235535 |
| work_keys_str_mv | AT gossonmauricede theprinciplesofnewtonianandquantummechanicstheneedforplancksconstanth AT gossonmauricede principlesofnewtonianandquantummechanicstheneedforplancksconstanth |