Quantization methods in differential equations
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Taylor & Francis
2002
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| Ausgabe: | 1. publ. |
| Schriftenreihe: | Differential and integral equations and their applications
3 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Nazajkinskij, Vladimir E. |d 1955- |e Verfasser |0 (DE-588)121444643 |4 aut | |
| 245 | 1 | 0 | |a Quantization methods in differential equations |c V. E. Nazaikinskii ; B.-W. Schulze ; B. Yu. Sternin |
| 250 | |a 1. publ. | ||
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| 300 | |a XII, 356 S. | ||
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Datensatz im Suchindex
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| adam_text | QUANTIZATION METHODS IN DIFFERENTIAL EQUATIONS V. . NAZAIKINSKII
INSTITUTE FOR PROBLEMS IN MECHANICS RUSSIAN ACADEMY OF SCIENCES MOSCOW,
RUSSIA B.-W. SCHULZE INSTITUTFUR MATHEMATIK UNIVERSITAT POTSDAM GERMANY
B. YU. STERNIN DEPARTMENT OF COMPUTER SCIENCE AND CYBERNETICS MOSCOW
STATE UNIVERSITY RUSSIA LONDON AND NEW YORK CONTENTS PREFACE IX ABOUT
THE AUTHORS X NOTATION XI INTRODUCTION 1 I SEMICLASSICAL QUANTIZATION 15
1 QUANTIZATION AND MICROLOCALIZATION 17 1.1 CLASSICAL MECHANICS AND
QUANTUM MECHANICS 17 1.2 THE CORRESPONDENCE PRINCIPLE AND THE
QUANTIZATION PROBLEM 23 1.3 COORDINATE AND MOMENTUM REPRESENTATIONS AND
THE FOURIER TRANSFORM 26 1.4 HAMILTONIANS 29 1.5 SEMICLASSICAL STATES 32
1.6 THE OSCILLATION FRONT AND THE PROBLEM OF MICROLOCAL ANALYSIS 37 2
QUANTIZATION BY THE WAVE PACKET TRANSFORM 45 2.1 QUANTIZATION OF PURE
STATES 45 2.2 THE WAVE PACKET TRANSFORM 51 2.3 QUANTIZATION OF
OBSERVABLES 59 2.4 QUANTIZATION OF MIXED STATES 71 2.5 QUANTIZATION OF
CANONICAL TRANSFORMATIONS 92 2.6 QUANTIZATION IN THE WAVE PACKET
REPRESENTATION 105 3 MASLOV S CANONICAL OPERATOR AND HORMANDER S
OSCILLATORY INTEGRALS 115 3.1 THE CLASSIFICATION PROBLEM FOR OSCILLATORY
INTEGRALS 115 3.2 TRANSFORMATIONS OF PHASE FUNCTIONS 117 3.3 THE LOCAL
CLASSIFICATION OF NONDEGENERATE PHASE FUNCTIONS. NORMAL FORMS 121 3.4
THE CLASSIFICATION OF OSCILLATORY INTEGRALS AND THE CANONICAL OPERATOR
131 3.5 SIMULTANEOUS ASYMPTOTICS 139 4 TOPOLOGICAL ASPECTS OF
QUANTIZATION CONDITIONS 143 4.1 CECH COCYCLES AND OBSTRUCTIONS TO THE
EXISTENCE OF THE CANONICAL OPERATOR 143 4.2 QUANTIZED MEASURES AND A
DIFFERENTIAL FORM REPRESENTING THE MASLOV-ARNOLD CLASS . 151 4.3 THE
INDEX OF PATHS ON LAGRANGIAN MANIFOLDS 154 4.4 QUANTIZATION OF
SYMPLECTIC MANIFOLDS 158 VI CONTENTS 5 THE SCHRODINGER EQUATION 167 5.1
THE CAUCHY PROBLEM 167 5.2 THE SPECTRUM ASYMPTOTICS 174 5.3 ASYMPTOTICS
OF THE GREEN FUNCTION 178 6 THE MAXWELL EQUATIONS 181 6.1 STATEMENT OF
THE PROBLEM 181 6.2 SOLUTION OF THE HOMOGENEOUS MAXWELL EQUATIONS 183
6.3 ASYMPTOTICS OF THE GREEN FUNCTION 190 6.4 SOLUTION OF THE
NONHOMOGENEOUS MAXWELL EQUATIONS 192 6.5 THE HELMHOLTZ EQUATION ON THE
SPHERE 197 7 EQUATIONS WITH TRAPPING HAMILTONIANS 201 7.1 STATEMENT OF
THE PROBLEM 201 7.2 A SCHEME FOR CONSTRUCTING THE REGULARIZER 203 7.3
THE CONTRIBUTION OF NONCLOSED TRAJECTORIES 205 7.4 THE CONTRIBUTION OF
CLOSED TRAJECTORIES 211 7.5 EXAMPLE: PROPAGATION OF SHORT
ELECTROMAGNETIC WAVES IN IONOSPHERE 213 II QUANTIZATION BY THE METHOD OF
ORDERED OPERATORS (NONCOMMUTATIVE ANALYSIS) 223 8 NONCOMMUTATIVE
ANALYSIS: MAIN IDEAS, DEFINITIONS, AND THEOREMS 225 8.1 FUNCTIONS OF ONE
OPERATOR 225 8.2 FUNCTIONS OF SEVERAL OPERATORS 228 8.3 MAIN FORMULAS OF
OPERATOR CALCULUS 234 8.4 MAIN TOOLS OF NONCOMMUTATIVE ANALYSIS 239 8.5
COMPOSITION LAWS AND ORDERED REPRESENTATIONS 247 9 EXACTLY SOLUBLE
COMMUTATION RELATIONS 257 9.1 STATEMENT OF THE PROBLEM 257 9.2 SOME
EXAMPLES 259 9.3 LIE COMMUTATION RELATIONS 270 9.4 NONLINEAR COMMUTATION
RELATIONS 276 10 OPERATOR ALGEBRAS ON SINGULAR MANIFOLDS 283 10.1
STATEMENT OF THE PROBLEM 283 10.2 OPERATORS ON THE MODEL CONE 291 10.3
OPERATORS ON THE MODEL CUSP OF ORDER A; 299 10.4 APPLICATION: THE
CONSTRUCTION OF REGULARIZERS AND PROOF OF THE FINITENESS THEOREM . . 303
11 THE HIGH-FREQUENCY ASYMPTOTICS IN THE PROBLEM OF WAVE PROPAGATION IN
PLASMA 313 11.1 STATEMENT OF THE PROBLEM 313 11.2 MIXED ASYMPTOTICS: THE
GENERAL SCHEME 315 11.3 THE ASYMPTOTIC SOLUTION OF THE MAIN PROBLEM .
318 11.4 ANALYSIS OF THE ASYMPTOTIC SOLUTION 324 CONTENTS VII APPENDICES
329 A COMPLEX PSEUDOCOORDINATES AND CLASSICAL MECHANICS 329 A. 1 COMPLEX
PSEUDOCOORDINATES 329 A.2 CLASSICAL MECHANICS IN COMPLEX
PSEUDOCOORDINATES 329 B SOME FORMULAS RELATED TO THE WAVE PACKET
TRANSFORM AND QUANTIZATION 333 BIBLIOGRAPHIC REMARKS 337 BIBLIOGRAPHY
345 INDEX 353
|
| any_adam_object | 1 |
| author | Nazajkinskij, Vladimir E. 1955- Schulze, Bert-Wolfgang 1944- Sternin, Boris Ju. 1939- |
| author_GND | (DE-588)121444643 (DE-588)120484579 (DE-588)120484536 |
| author_facet | Nazajkinskij, Vladimir E. 1955- Schulze, Bert-Wolfgang 1944- Sternin, Boris Ju. 1939- |
| author_role | aut aut aut |
| author_sort | Nazajkinskij, Vladimir E. 1955- |
| author_variant | v e n ve ven b w s bws b j s bj bjs |
| building | Verbundindex |
| bvnumber | BV014597395 |
| classification_rvk | SK 500 SK 540 |
| ctrlnum | (OCoLC)470113009 (DE-599)BVBBV014597395 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV014597395 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:04:05Z |
| institution | BVB |
| isbn | 0415273641 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009921267 |
| oclc_num | 470113009 |
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| physical | XII, 356 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Taylor & Francis |
| record_format | marc |
| series | Differential and integral equations and their applications |
| series2 | Differential and integral equations and their applications |
| spelling | Nazajkinskij, Vladimir E. 1955- Verfasser (DE-588)121444643 aut Quantization methods in differential equations V. E. Nazaikinskii ; B.-W. Schulze ; B. Yu. Sternin 1. publ. London [u.a.] Taylor & Francis 2002 XII, 356 S. txt rdacontent n rdamedia nc rdacarrier Differential and integral equations and their applications 3 Quantification géométrique ram Équations aux dérivées partielles linéaires ram Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd rswk-swf Quantisierung Physik (DE-588)4176603-9 gnd rswk-swf Lineare partielle Differentialgleichung (DE-588)4167708-0 s Quantisierung Physik (DE-588)4176603-9 s DE-604 Schulze, Bert-Wolfgang 1944- Verfasser (DE-588)120484579 aut Sternin, Boris Ju. 1939- Verfasser (DE-588)120484536 aut Differential and integral equations and their applications 3 (DE-604)BV014412675 3 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009921267&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nazajkinskij, Vladimir E. 1955- Schulze, Bert-Wolfgang 1944- Sternin, Boris Ju. 1939- Quantization methods in differential equations Differential and integral equations and their applications Quantification géométrique ram Équations aux dérivées partielles linéaires ram Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Quantisierung Physik (DE-588)4176603-9 gnd |
| subject_GND | (DE-588)4167708-0 (DE-588)4176603-9 |
| title | Quantization methods in differential equations |
| title_auth | Quantization methods in differential equations |
| title_exact_search | Quantization methods in differential equations |
| title_full | Quantization methods in differential equations V. E. Nazaikinskii ; B.-W. Schulze ; B. Yu. Sternin |
| title_fullStr | Quantization methods in differential equations V. E. Nazaikinskii ; B.-W. Schulze ; B. Yu. Sternin |
| title_full_unstemmed | Quantization methods in differential equations V. E. Nazaikinskii ; B.-W. Schulze ; B. Yu. Sternin |
| title_short | Quantization methods in differential equations |
| title_sort | quantization methods in differential equations |
| topic | Quantification géométrique ram Équations aux dérivées partielles linéaires ram Lineare partielle Differentialgleichung (DE-588)4167708-0 gnd Quantisierung Physik (DE-588)4176603-9 gnd |
| topic_facet | Quantification géométrique Équations aux dérivées partielles linéaires Lineare partielle Differentialgleichung Quantisierung Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009921267&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014412675 |
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