The principles of Newtonian and quantum mechanics: the need for Planck's constant, h
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 357 S. |
| ISBN: | 1860942741 |
Staff View
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| 245 | 1 | 0 | |a The principles of Newtonian and quantum mechanics |b the need for Planck's constant, h |c M. A. de Gosson |
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Record in the Search Index
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| adam_text | THE PRINCIPLES OF NEWTONIAN AND QUANTUM MECHANICS THE NEED FOR PLANCK S
CONSTANT, H MADE GOSSON BLEKINGE INSTITUTE OF TECHNOLOGY, SWEDEN
IMPERIAL COLLEGE PRESS CONTENTS 1 FROM KEPLER TO SCHRODINGER ... AND
BEYOND 1 1.1 CLASSICAL MECHANICS 2 1.1.1 NEWTON S LAWS AND MACH S
PRINCIPLE 1.1.2 MASS, FORCE, AND MOMENTUM 1.2 SYMPLECTIC MECHANICS 6
1.2.1 HAMILTON S EQUATIONS 1.2.2 GAUGE TRANSFORMATIONS 1.2.3 HAMILTONIAN
FIELDS AND FLOWS 1.2.4 THE SYMPLECTIZATION OF SCIENCE 1.3 ACTION AND
HAMILTON-JACOBI S THEORY 11 1.3.1 ACTION 1.3.2 HAMILTON-JACOBI S
EQUATION 1.4 QUANTUM MECHANICS 13 1.4.1 MATTER WAVES 1.4.2 IF THERE IS
A WAVE, THERE MUST BE A WAVE EQUATION! 1.4.3 SCHRODINGER S QUANTIZATION
RULE AND GEOMETRIC QUANTIZATION 1.5 THE STATISTICAL INTERPRETATION OF *
19 1.5.1 HEISENBERG S INEQUALITIES 1.6 QUANTUM MECHANICS IN PHASE SPACE
22 1.6.1 SCHRODINGER S FIREFLY ARGUMENT 1.6.2 THE SYMPLECTIC CAMEL 1.7
FEYNMAN S PATH INTEGRAL 25 1.7.1 THE SUM OVER ALL PATHS 1.7.2 THE
METAPLECTIC GROUP 1.8 BOHMIAN MECHANICS 27 1.8.1 QUANTUM MOTION: THE
BELL-DGZ THEORY 1.8.2 BOHM S THEORY XVIII CONTENTS 1.9 INTERPRETATIONS
31 1.9.1 EPISTEMOLOGY OR ONTOLOGY? 1.9.2 THE COPENHAGEN INTERPRETATION
1.9.3 THE BOHMIAN INTERPRETATION 1.9.4 THE PLATONIC POINT OF VIEW 2
NEWTONIAN MECHANICS 37 2.1 MAXWELL S PRINCIPLE AND THE LAGRANGE FORM 37
2.1.1 THE HAMILTON VECTOR FIELD 2.1.2 FORCE FIELDS 2.1.3 STATEMENT OF
MAXWELL S PRINCIPLE 2.1.4 MAGNETIC MONOPOLES AND THE DIRAC STRING 2.1.5
THE LAGRANGE FORM 2.1.6 IV-PARTICLE SYSTEMS 2.2 HAMILTON S EQUATIONS 49
2.2.1 THE POINCARE-CARTAN FORM AND HAMILTON S EQUATIONS 2.2.2
HAMILTONIANS FOR IV-PARTICLE SYSTEMS 2.2.3 THE TRANSFORMATION LAW FOR
HAMILTON VECTOR FIELDS 2.2.4 THE SUSPENDED HAMILTONIAN VECTOR FIELD 2.3
GALILEAN COVARIANCE 58 2.3.1 INERTIAL FRAMES 2.3.2 THE GALILEAN GROUP
GAL(3) 2.3.3 GALILEAN COVARIANCE OF HAMILTON S EQUATIONS 2.4 CONSTANTS
OF THE MOTION AND INTEGRABLE SYSTEMS 65 2.4.1 THE POISSON BRACKET 2.4.2
CONSTANTS OF THE MOTION AND LIOUVILLE S EQUATION 2.4.3 CONSTANTS OF THE
MOTION IN INVOLUTION 2.5 LIOUVILLE S EQUATION AND STATISTICAL MECHANICS
70 2.5.1 LIOUVILLE S CONDITION 2.5.2 MARGINAL PROBABILITIES 2.5.3
DISTRIBUTIONAL DENSITIES: AN EXAMPLE 3 THE SYMPLECTIC GROUP 77 3.1
SYMPLECTIC MATRICES AND SP(N) 77 3.2 SYMPLECTIC INVARIANCE OF
HAMILTONIAN FLOWS 80 3.2.1 NOTATIONS AND TERMINOLOGY 3.2.2 PROOF OF THE
SYMPLECTIC INVARIANCE OF HAMILTONIAN FLOWS 3.2.3 ANOTHER PROOF OF THE
SYMPLECTIC INVARIANCE OF FLOWS* 3.3 THE PROPERTIES OF SP(N) 83 CONTENTS
XIX 3.3.1 THE SUBGROUPS U(N) AND O(N) OF SP(N) 3.3.2 THE LIE ALGEBRA
SP(N) 3.3.3 SP(N) AS A LIE GROUP 3.4 QUADRATIC HAMILTONIANS 88 3.4.1 THE
LINEAR SYMMETRIC TRIATOMIC MOLECULE 3.4.2 ELECTRON IN A UNIFORM MAGNETIC
FIELD 3.5 THE INHOMOGENEOUS SYMPLECTIC GROUP 92 3.5.1 GALILEAN
TRANSFORMATIONS AND ISP(N) 3.6 AN ILLUMINATING ANALOGY - 94 3.6.1 THE
OPTICAL HAMILTONIAN 3.6.2 PARAXIAL OPTICS 3.7 GROMOV S NON-SQUEEZING
THEOREM , 99 3.7.1 LIOUVILLE S THEOREM REVISITED 3.7.2 GROMOV S THEOREM
3.7.3 THE UNCERTAINTY PRINCIPLE IN CLASSICAL MECHANICS 3.8 SYMPLECTIC
CAPACITY AND PERIODIC ORBITS 108 3.8.1 THE CAPACITY OF AN ELLIPSOID
3.8.2 SYMPLECTIC AREA AND VOLUME 3.9 CAPACITY AND PERIODIC ORBITS 113
3.9.1 PERIODIC HAMILTONIAN ORBITS 3.9.2 ACTION OF PERIODIC ORBITS AND
CAPACITY 3.10 CELL QUANTIZATION OF PHASE SPACE 118 3.10.1 STATIONARY
STATES OF SCHRODINGER S EQUATION 3.10.2 QUANTUM CELLS AND THE MINIMUM
CAPACITY PRINCIPLE 3.10.3 QUANTIZATION OF THE IV-DIMENSIONAL HARMONIC
OSCILLATOR 4 ACTION AND PHASE 127 4.1 INTRODUCTION 127 4.2 THE
FUNDAMENTAL PROPERTY OF THE POINCARE-CARTAN FORM 128 4.2.1 HELMHOLTZ S
THEOREM: THE CASE N = 1 4.2.2 HELMHOLTZ S THEOREM: THE GENERAL CASE 4.3
FREE SYMPLECTOMORPHISMS AND GENERATING FUNCTIONS 132 4.3.1 GENERATING
FUNCTIONS 4.3.2 OPTICAL ANALOGY: THE EIKONAL 4.4 GENERATING FUNCTIONS
AND ACTION 137 4.4.1 THE GENERATING FUNCTION DETERMINED BY H 4.4.2
ACTION VS. GENERATING FUNCTION : 4.4.3 GAUGE TRANSFORMATIONS AND
GENERATING FUNCTIONS XX CONTENTS 4.4.4 SOLVING HAMILTON S EQUATIONS WITH
W 4.4.5 THE CAUCHY PROBLEM FOR HAMILTON-JACOBI S EQUATION 4.5 SHORT-TIME
APPROXIMATIONS TO THE ACTION 147 4.5.1 THE CASE OF A SCALAR POTENTIAL
4.5.2 ONE PARTICLE IN A GAUGE (A, U) 4.5.3 MANY-PARTICLE SYSTEMS IN A
GAUGE (A, U) 4.6 LAGRANGIAN MANIFOLDS 156 4.6.1 DEFINITIONS AND BASIC
PROPERTIES 4.6.2 LAGRANGIAN MANIFOLDS IN MECHANICS 4.7 THE PHASE OF A
LAGRANGIAN MANIFOLD 161 4.7.1 THE PHASE OF AN EXACT LAGRANGIAN MANIFOLD
4.7.2 THE UNIVERSAL COVERING OF A MANIFOLD* 4.7.3 THE PHASE: GENERAL
CASE 4.7.4 PHASE AND HAMILTONIAN MOTION 4.8 KELLER-MASLOV QUANTIZATION
168 4.8.1 THE MASLOV INDEX FOR LOOPS 4.8.2 QUANTIZATION OF LAGRANGIAN
MANIFOLDS 4.8.3 ILLUSTRATION: THE PLANE ROTATOR 5 SEMI-CLASSICAL
MECHANICS 179 5.1 BOHMIAN MOTION AND HALF-DENSITIES 179 5.1.1 WAVE-FORMS
ON EXACT LAGRANGIAN MANIFOLDS 5.1.2 SEMI-CLASSICAL MECHANICS 5.1.3
WAVE-FORMS: INTRODUCTORY EXAMPLE 5.2 THE LERAY INDEX AND THE SIGNATURE
FUNCTION* 186 5.2.1 COHOMOLOGICAL NOTATIONS 5.2.2 THE LERAY INDEX: N = 1
5.2.3 THE LERAY INDEX: GENERAL CASE 5.2.4 PROPERTIES OF THE LERAY INDEX
5.2.5 MORE ON THE SIGNATURE FUNCTION 5.2.6 THE REDUCED LERAY INDEX 5.3
DE RHAM FORMS 201 5.3.1 VOLUMES AND THEIR ABSOLUTE VALUES 5.3.2
CONSTRUCTION OF DE RHAM FORMS ON MANIFOLDS 5.3.3 DE RHAM FORMS ON
LAGRANGIAN MANIFOLDS 5.4 WAVE-FORMS ON A LAGRANGIAN MANIFOLD 212 5.4.1
DEFINITION OF WAVE FORMS 5.4.2 THE CLASSICAL MOTION OF WAVE-FORMS
CONTENTS XXI 5.4.3. THE SHADOW OF A WAVE-FORM 6 THE METAPLECTIC GROUP
AND THE MASLOV INDEX 221 6.1 INTRODUCTION 221 6.1.1 COULD SCHRODINGER
HAVE DONE IT RIGOROUSLY? 6.1.2 SCHRODINGER S IDEA 6.1.3 SP{NYS BIG
BROTHER MP(N) 6.2 FREE SYMPLECTIC MATRICES AND THEIR GENERATING
FUNCTIONS 225 6.2.1 FREE SYMPLECTIC MATRICES 6.2.2 THE CASE OF AFFINE
SYMPLECTOMORPHISMS 6.2.3 THE GENERATORS OF SPIN) 6.3 THE METAPLECTIC
GROUP MPIN) 231 6.3.1 QUADRATIC FOURIER TRANSFORMS 6.3.2 THE OPERATORS M
L AND V P 6.4 THE PROJECTIONS N AND W 237 6.4.1 CONSTRUCTION OF THE
PROJECTION II 6.4.2 THE COVERING GROUPS MP IN) 6.5 THE MASLOV INDEX ON
MPIN) 242 6.5.1 MASLOV INDEX: A SIMPLE EXAMPLE 6.5.2 DEFINITION OF THE
MASLOV INDEX ON MPIN) 6.6 THE COHOMOLOGICAL MEANING OF THE MASLOV INDEX*
247 6.6.1 GROUP COCYCLES ON SPIN) 6.6.2 THE FUNDAMENTAL PROPERTY OF M(-)
6.7 THE INHOMOGENEOUS METAPLECTIC GROUP 253 6.7.1 THE HEISENBERG GROUP
6.7.2 THE GROUP IMP{N) 6.8 THE METAPLECTIC GROUP AND WAVE OPTICS 258
6.8.1 THE PASSAGE FROM GEOMETRIC TO WAVE OPTICS 6.9 THE GROUPS SYMPIN)
AND HAMIN)* 260 6.9.1 A TOPOLOGICAL PROPERTY OF SYMPIN) 6.9.2 THE GROUP
HAMIN) OF HAMILTONIAN SYMPLECTOMORPHISMS 6.9.3 THE GROENEWOLD-VAN HOVE
THEOREM 7 SCHRODINGER S EQUATION AND THE METATRON 267 7.1 SCHRODINGER S
EQUATION FOR THE FREE PARTICLE 267 7.1.1 THE FREE PARTICLE S PHASE 7.1.2
THE FREE PARTICLE PROPAGATOR 7.1.3 AN EXPLICIT EXPRESSION FOR G XXII
CONTENTS 7.1.4 THE METAPLECTIC REPRESENTATION OF THE FREE FLOW 7.1.5
MORE QUADRATIC HAMILTONIANS 7.2 VAN VLECK S DETERMINANT 277 7.2.1
TRAJECTORY DENSITIES 7.3 THE CONTINUITY EQUATION FOR VAN VLECK S DENSITY
280 7.3.1 A PROPERTY OF DIFFERENTIAL SYSTEMS 7.3.2 THE CONTINUITY
EQUATION FOR VAN VLECK S DENSITY 7.4 THE SHORT-TIME PROPAGATOR 284 7.4.1
PROPERTIES OF THE SHORT-TIME PROPAGATOR 7.5 THE CASE OF QUADRATIC
HAMILTONIANS 288 7.5.1 EXACT GREEN FUNCTION 7.5.2 EXACT SOLUTIONS OF
SCHRODINGER S EQUATION 7.6 SOLVING SCHRODINGER S EQUATION: GENERAL CASE
290 7.6.1 THE SHORT-TIME PROPAGATOR AND CAUSALITY 7.6.2 STATEMENT OF THE
MAIN THEOREM 7.6.3 THE FORMULA OF STATIONARY PHASE 7.6.4 TWO LEMMAS *
AND THE PROOF 7.7 METATRONS AND THE IMPLICATE ORDER 300 7.7.1 UNFOLDING
AND IMPLICATE ORDER 7.7.2 PREDICTION AND RETRODICTION 7.7.3 THE
LIE-TROTTER FORMULA FOR FLOWS 7.7.4 THE UNFOLDED METATRON 7.7.5 THE
GENERALIZED METAPLECTIC REPRESENTATION 7.8 PHASE SPACE AND SCHRODINGER S
EQUATION 313 7.8.1 PHASE SPACE AND QUANTUM MECHANICS 7.8.2 MIXED
REPRESENTATIONS IN QUANTUM MECHANICS 7.8.3 COMPLEMENTARITY AND THE
IMPLICATE ORDER A SYMPLECTIC LINEAR ALGEBRA 323 B THE LIE-TROTTER
FORMULA FOR FLOWS 327 C THE HEISENBERG GROUPS 331 D THE BUNDLE OF
S-DENSITIES 335 E THE LAGRANGIAN GRASSMANNIAN 339 BIBLIOGRAPHY 343 INDEX
353
|
| any_adam_object | 1 |
| author | Gosson, Maurice A. de 1948- |
| author_GND | (DE-588)1024136949 |
| author_facet | Gosson, Maurice A. de 1948- |
| author_role | aut |
| author_sort | Gosson, Maurice A. de 1948- |
| author_variant | m a d g mad madg |
| building | Verbundindex |
| bvnumber | BV014086241 |
| callnumber-first | Q - Science |
| callnumber-label | QC20 |
| callnumber-raw | QC20.7.C3 |
| callnumber-search | QC20.7.C3 |
| callnumber-sort | QC 220.7 C3 |
| callnumber-subject | QC - Physics |
| classification_rvk | UF 1000 UK 1000 UK 1200 |
| classification_tum | PHY 022f PHY 011f |
| ctrlnum | (OCoLC)46777436 (DE-599)BVBBV014086241 |
| 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 | Book |
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| id | DE-604.BV014086241 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:57:24Z |
| institution | BVB |
| isbn | 1860942741 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009649291 |
| oclc_num | 46777436 |
| open_access_boolean | |
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| owner_facet | DE-355 DE-BY-UBR DE-384 DE-703 DE-19 DE-BY-UBM DE-11 DE-91G DE-BY-TUM |
| physical | XXII, 357 S. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Gosson, Maurice A. de 1948- Verfasser (DE-588)1024136949 aut The principles of Newtonian and quantum mechanics the need for Planck's constant, h M. A. de Gosson London Imperial College Press 2001 XXII, 357 S. txt rdacontent n rdamedia nc rdacarrier Geometric quantization Lagrangian functions Maslov index Lagrange-Funktion (DE-588)4166459-0 gnd rswk-swf Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Mechanik (DE-588)4038168-7 gnd rswk-swf Maslov-Index (DE-588)4169023-0 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Lagrange-Funktion (DE-588)4166459-0 s Maslov-Index (DE-588)4169023-0 s Geometrische Quantisierung (DE-588)4156720-1 s DE-604 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 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009649291&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gosson, Maurice A. de 1948- The principles of Newtonian and quantum mechanics the need for Planck's constant, h Geometric quantization Lagrangian functions Maslov index Lagrange-Funktion (DE-588)4166459-0 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd Symplektische Geometrie (DE-588)4194232-2 gnd Quantenmechanik (DE-588)4047989-4 gnd Mechanik (DE-588)4038168-7 gnd Maslov-Index (DE-588)4169023-0 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4166459-0 (DE-588)4156720-1 (DE-588)4194232-2 (DE-588)4047989-4 (DE-588)4038168-7 (DE-588)4169023-0 (DE-588)4037952-8 |
| 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 | Geometric quantization Lagrangian functions Maslov index Lagrange-Funktion (DE-588)4166459-0 gnd Geometrische Quantisierung (DE-588)4156720-1 gnd Symplektische Geometrie (DE-588)4194232-2 gnd Quantenmechanik (DE-588)4047989-4 gnd Mechanik (DE-588)4038168-7 gnd Maslov-Index (DE-588)4169023-0 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Geometric quantization Lagrangian functions Maslov index Lagrange-Funktion Geometrische Quantisierung Symplektische Geometrie Quantenmechanik Mechanik Maslov-Index Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009649291&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gossonmauriceade theprinciplesofnewtonianandquantummechanicstheneedforplancksconstanth |