Angular momentum techniques in quantum mechanics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1999
|
| Schriftenreihe: | Fundamental theories of physics
108 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 242 S. |
| ISBN: | 079235866X |
Internformat
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| 245 | 1 | 0 | |a Angular momentum techniques in quantum mechanics |c by V. Devanathan |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1999 | |
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| 490 | 1 | |a Fundamental theories of physics |v 108 | |
| 650 | 4 | |a Moment angulaire | |
| 650 | 4 | |a Théorie quantique | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Angular momentum | |
| 650 | 4 | |a Quantum theory | |
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Datensatz im Suchindex
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|---|---|
| adam_text | ANGULAR MOMENTUM TECHNIQUES IN QUANTUM MECHANICS BY V. DEVANATHAN
DEPARTMENT OF NUCLEAR PHYSICS, UNIVERSITY OF MADRAS AND CRYSTAL GROWTH
CENTRE, ANNA UNIVERSITY, CHENNAI, INDIA KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON CONTENTS PREFACE XIII 1 ANGULAR MOMENTUM
OPERATORS AND THEIR MATRIX ELEMENTS 1 1.1 QUANTUM MECHANICAL DEFINITION
1 1.2 PHYSICAL INTERPRETATION OF ANGULAR MOMENTUM VECTOR ... 2 1.3
RAISING AND LOWERING OPERATORS . 3 1.4 SPECTRUM OF EIGENVALUES 4 1.5
MATRIX ELEMENTS 5 1.6 ANGULAR MOMENTUM MATRICES 6 REVIEW QUESTIONS 8
PROBLEMS 8 SOLUTIONS TO SELECTED PROBLEMS 9 2 COUPLING OF TWO ANGULAR
MOMENTA 10 2.1 THE CLEBSCH-GORDAN COEFFICIENTS 10 2.2 SOME SIMPLE
PROPERTIES OF C.G. COEFFICIENTS 11 2.3 GENERAL EXPRESSIONS FOR C.G.
COEFFICIENTS 13 2.4 SYMMETRY PROPERTIES OF C.G. COEFFICIENTS 14 2.5
ISO-SPIN 15 2.6 NOTATION 16 REVIEW QUESTIONS 16 PROBLEMS 17 SOLUTIONS TO
SELECTED PROBLEMS 19 3 VECTORS AND TENSORS IN SPHERICAL BASIS 24 3.1 THE
SPHERICAL BASIS 24 3.2 SCALAR AND VECTOR PRODUCTS IN SPHERICAL BASIS 26
3.3 THE SPHERICAL TENSORS 27 3.4 THE TENSOR PRODUCT 29 REVIEW QUESTIONS
30 PROBLEMS 31 SOLUTIONS TO SELECTED PROBLEMS 31 VII VIA 4 ROTATION
MATRICES - I 34 4.1 DEFINITION OF ROTATION MATRIX 34 4.2 ROTATION IN
TERMS OF EULER ANGLES 34 4.3 TRANSFORMATION OF A SPHERICAL VECTOR UNDER
ROTATION OF COORDINATE SYSTEM 35 4.4 THE ROTATION MATRIX D A, SS,J) 38
4.5 CONSTRUCTION OF OTHER ROTATION MATRICES 38 REVIEW QUESTIONS 39
PROBLEMS 39 SOLUTIONS TO SELECTED PROBLEMS 39 5 ROTATION MATRICES - II
42 5.1 THE ROTATION OPERATOR 42 5.2 THE D? M , M {SS) MATRIX 44 5.3 THE
ROTATION MATRIX FOR SPINORS 45 5.4 THE CLEBSCH-GORDAN SERIES 48 5.5 THE
INVERSE CLEBSCH-GORDAN SERIES 49 5.6 UNITARITY AND SYMMETRY PROPERTIES
OF THE ROTATION MATRICES 50 5.7 THE SPHERICAL HARMONIC ADDITION THEOREM
52 5.8 THE COUPLING RULE FOR THE SPHERICAL HARMONICS 54 5.9
ORTHOGONALITY AND NORMALIZATION OF THE ROTATION MATRICES . 56 REVIEW
QUESTIONS 57 PROBLEMS 58 SOLUTIONS TO SELECTED PROBLEMS 58 6 TENSOR
OPERATORS AND REDUCED MATRIX ELEMENTS 61 6.1 IRREDUCIBLE TENSOR
OPERATORS 61 6.2 RACAH S DEFINITION 61 6.3 THE WIGNER-ECKART THEOREM 63
6.4 PROOFS OF THE WIGNER-ECKART THEOREM 65 6.4.1 METHOD I 65 6.4.2
METHOD II 67 6.4.3 METHOD III 69 6.5 TENSORS AND TENSOR OPERATORS 72
REVIEW QUESTIONS 74 PROBLEMS 75 SOLUTIONS TO SELECTED PROBLEMS 75 7
COUPLING OF THREE ANGULAR MOMENTA 77 7.1 DEFINITION OF THE U-COEFFICIENT
77 7.2 THE U-COEFFICIENT IN TERMS OF CG. COEFFICIENTS 78 IX 7.3
INDEPENDENCE OF U-COEFFICIENT FROM MAGNETIC QUANTUM NUMBERS 79 7.4
ORTHONORMALITY OF THE U-COEFFICIENTS 80 7.5 THE RACAH COEFFICIENT AND
ITS SYMMETRY PROPERTIES . . . . 81 7.6 EVALUATION OF MATRIX ELEMENTS 82
REVIEW QUESTIONS 85 PROBLEMS 85 SOLUTIONS TO SELECTED PROBLEMS 85 8
COUPLING OF FOUR ANGULAR MOMENTA 88 8.1 DEFINITION OF LS-JJ COUPLING
COEFFICIENT 88 8.2 LS-JJ COUPLING COEFFICIENT IN TERMS OF C.G.
COEFFICIENTS ... 89 8.3 INDEPENDENCE OF THE LS-JJ COUPLING COEFFICIENTS
FROM THE MAGNETIC QUANTUM NUMBERS 91 8.4 SIMPLE PROPERTIES 92 8.5
EXPANSION OF 9-J SYMBOL INTO RACAH COEFFICIENTS 93 8.6 EVALUATION OF
MATRIX ELEMENTS 95 REVIEW QUESTIONS 96 PROBLEMS 96 SOLUTIONS TO SELECTED
PROBLEMS 97 9 PARTIAL WAVES AND THE GRADIENT FORMULA 100 9.1 PARTIAL
WAVE EXPANSION FOR A PLANE WAVE 100 9.2 DISTORTED WAVES 102 9.3 THE
GRADIENT FORMULA 103 9.4 DERIVATION OF THE GRADIENT FORMULA 105 9.5
MATRIX ELEMENTS INVOLVING THE V OPERATOR 108 REVIEW QUESTIONS 112
PROBLEMS 113 SOLUTIONS TO SELECTED PROBLEMS 114 10 IDENTICAL PARTICLES
119 10.1 FERMIONS AND BOSONS 119 10.2 TWO IDENTICAL FERMIONS IN J-J
COUPLING 119 10.3 CONSTRUCTION OF THREE-FERMION WAVE FUNCTION 120 10.4
CALCULATION OF FRACTIONAL PARENTAGE COEFFICIENTS 123 10.5 THE ISO-SPIN
125 10.6 THE BOSONS 126 10.7 THE M-SCHEME 126 REVIEW QUESTIONS 128
PROBLEMS 128 SOLUTIONS TO SELECTED PROBLEMS 129 X 11 DENSITY MATRIX AND
STATISTICAL TENSORS 130 11.1 CONCEPT OF THE DENSITY MATRIX 130 11.2
CONSTRUCTION OF THE DENSITY MATRIX 133 11.3 FANO S STATISTICAL TENSORS
134 11.4 ORIENTED AND NON-ORIENTED SYSTEMS 139 11.5 APPLICATION TO
NUCLEAR REACTIONS 140 REVIEW QUESTIONS 144 PROBLEMS 145 SOLUTIONS TO
SELECTED PROBLEMS 146 12 PRODUCTS OF ANGULAR MOMENTUM MATRICES AND THEIR
TRACES 150 12.1 GENERAL PROPERTIES * 150 12.2 EVALUATION OF TR J 2ZP 152
12.3 EVALUATION OF TR (JTJ%) 155 12.4 RECURRENCE RELATIONS FOR TR {J K
_J LZ JD 157 12.5 SOME SIMPLE APPLICATIONS 158 12.5.1 STATISTICAL
TENSORS 158 12.5.2 CONSTRUCTION OF TJJ 159 12.5.3 ANALYTICAL EXPRESSION
FOR (J* /) 160 12.5.4 ELASTIC SCATTERING OF PARTICLES OF ARBITRARY SPIN
... 161 REVIEW QUESTIONS 162 PROBLEMS 162 SOLUTIONS TO SELECTED PROBLEMS
163 13 THE HELICITY FORMALISM 165 13.1 THE HELICITY STATES 165 13.2
TWO-PARTICLE HELICITY STATES 171 13.3 SCATTERING OF PARTICLES WITH SPIN
172 13.3.1 SCATTERING CROSS SECTION 172 13.3.2 INVARIANCE UNDER PARITY
AND TIME REVERSAL 175 13.3.3 POLARIZATION STUDIES 176 13.4 TWO-BODY
DECAY 181 13.5 MUON CAPTURE 191 REVIEW QUESTIONS 195 PROBLEMS 195
SOLUTIONS TO SELECTED PROBLEMS 196 14 THE SPIN STATES OF DIRAC PARTICLES
199 14.1 THE DIRAC EQUATION 199 14.2 ORTHOGONAL AND CLOSURE PROPERTIES
201 14.3 SUM OVER SPIN STATES 203 XI 14.4 IN FEYNMAN S NOTATION 206 14.5
A CONSISTENCY CHECK . 209 14.6 ALGEBRA OF 7 MATRICES 210 REVIEW
QUESTIONS 213 PROBLEMS 213 SOLUTIONS TO SELECTED PROBLEMS 213 APPENDIX A
EQUIVALENCE OF ROTATION ABOUT AN ARBITRARY AXIS TO EULER ANGLES OF
ROTATION 216 APPENDIX * TABLES OF CLEBSCH-GORDON COEFFICIENTS 224
APPENDIX * TABLES OF RACAH COEFFICIENTS 225 APPENDIX D SPHERICAL
HARMONICS 227 APPENDIX E THE SPHERICAL BESSEL AND NEUMANN FUNCTIONS 230
APPENDIX F THE BERNOULLI POLYNOMIALS 232 APPENDIX G LIST OF SYMBOLS AND
NOTATION 234 REFERENCES 238 SUBJECT INDEX 241
|
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| indexdate | 2024-07-09T18:38:18Z |
| institution | BVB |
| isbn | 079235866X |
| language | English |
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| physical | XIV, 242 S. |
| publishDate | 1999 |
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| publisher | Kluwer |
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| series | Fundamental theories of physics |
| series2 | Fundamental theories of physics |
| spelling | Devanathan, Varadarajan Verfasser aut Angular momentum techniques in quantum mechanics by V. Devanathan Dordrecht [u.a.] Kluwer 1999 XIV, 242 S. txt rdacontent n rdamedia nc rdacarrier Fundamental theories of physics 108 Moment angulaire Théorie quantique Quantentheorie Angular momentum Quantum theory Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Drehimpuls (DE-588)4150572-4 gnd rswk-swf Drehimpuls (DE-588)4150572-4 s Quantenmechanik (DE-588)4047989-4 s DE-604 Fundamental theories of physics 108 (DE-604)BV000012461 108 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008892609&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Devanathan, Varadarajan Angular momentum techniques in quantum mechanics Fundamental theories of physics Moment angulaire Théorie quantique Quantentheorie Angular momentum Quantum theory Quantenmechanik (DE-588)4047989-4 gnd Drehimpuls (DE-588)4150572-4 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4150572-4 |
| title | Angular momentum techniques in quantum mechanics |
| title_auth | Angular momentum techniques in quantum mechanics |
| title_exact_search | Angular momentum techniques in quantum mechanics |
| title_full | Angular momentum techniques in quantum mechanics by V. Devanathan |
| title_fullStr | Angular momentum techniques in quantum mechanics by V. Devanathan |
| title_full_unstemmed | Angular momentum techniques in quantum mechanics by V. Devanathan |
| title_short | Angular momentum techniques in quantum mechanics |
| title_sort | angular momentum techniques in quantum mechanics |
| topic | Moment angulaire Théorie quantique Quantentheorie Angular momentum Quantum theory Quantenmechanik (DE-588)4047989-4 gnd Drehimpuls (DE-588)4150572-4 gnd |
| topic_facet | Moment angulaire Théorie quantique Quantentheorie Angular momentum Quantum theory Quantenmechanik Drehimpuls |
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