Quantum theory of angular momentum: irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
1989
|
| Edition: | 1. reprint |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | X, 514 S. |
| ISBN: | 9971501074 9971509962 |
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MARC
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| 100 | 1 | |a Varšalovič, Dimitrij A. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Kvantovaja teorija uglovogo momenta |
| 245 | 1 | 0 | |a Quantum theory of angular momentum |b irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols |c D. A. Varshalovich ; A. N. Moskalev ; V. K. Khersonskii |
| 250 | |a 1. reprint | ||
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1989 | |
| 300 | |a X, 514 S. | ||
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| 700 | 1 | |a Chersonskij, Valerij K. |e Verfasser |4 aut | |
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| _version_ | 1804128158335631360 |
|---|---|
| adam_text | Titel: Quantum theory of angular momentum
Autor: Varšalovič, Dmitrij A
Jahr: 1989
CONTENTS
Preface v
Introduction: Basic Concepts 1
Chapter 1. Elements of Vector and Tensor Theory 3
1.1. Coordinate Systems. Basis Vectors 3
1.2. Vectors. Tensors 11
1.3. Differential Operations 17
1.4. Rotations of Coordinate System 21
Chapter 2. Angular MOmentum Operators 36
2.1. Total Angular Momentum Operator 36
2.2. Orbital Angular Momentum Operator 39
2.3. Spin Angular Momentum Operator 42
2.4. Polarisation Operators 44
2.5. Spin Matrices for S = | 47
2.6. Spin Matrices and Polarisation Operators for 5 = 1 51
Chapter 3. Irreducible Tensors 61
3.1. Definition and Properties of Irreducible Tensors 61
3.2. Relation Between the Irreducible Tensor Algebra and Vector and Tensor Theory . . 65
3.3. Recoupling in Irreducible Tensor Products 69
Chapter 4. Wigner D-Functions 72
4.1. Definition of 72
4.2. Differential Equations for D%fM (aiß l) ^
4.3. Explicit Forms of the Wigner D-Functions 76
4.4. Symmetries of dJMM,[ß) and DlfM,{a,ß,i) 79
4.5. Rotation Matrix U^fM, in Terms of Angles w, 0, $ 80
4.6. Sums Involving D-Functions 84
4.7. Addition of Rotations 87
4.8. Recursion Relations for Dj^M, 90
vii
viii Contents
4.9. Differential Relations for D^Mi (a, ß,i) 94
4.10. Orthogonality and Completeness of the D-Functions 94
4.11. Integrals Involving the D-Functions 96
4.12. Invariant Summation of Integrals Involving ß, i) 97
4.13. Generating Functions for dj^M,{ß) 98
4.14. Characters xJ(-ß) °f Irreducible Representations of Rotation Group 99
4.15. Generalized Characters, X {R) of Irreducible Representations of the Rotation Group 106
4.16. Djmm, (a,ß,i) for Particular Values of the Arguments 112
4.17. Special Cases of DJMM,{a.,ß,i) for Particular Af or M 113
4.18. Asymptotics of Djll(M,{a,ß,ni) 115
4.19. Definitions of Mi{ot,ß,i) by Other Authors 117
4.20. Special Cases of dlfM,(ß) for Particular J,M and M 117
4.21. Tables of dJMM,{ß) for ß = jt/2 .117
4.22. Special Cases of 8,$) 117
Chapter 5. Spherical Harmonics 130
5.1. Definition 130
5.2. Explicit Forms of the Spherical Harmonics and Their Relations to Other Functions 133
5.3. Integral Representations of the Spherical Harmonics [4, 22, 27] 139
5.4. Symmetry Properties 140
5.5. Behaviour of p) under Transformations of Coordinate Systems 141
5.6. Expansions in Series of the Spherical Harmonics 143
5.7. Recursion Relations 145
5.8. Differential Relations 146
5.9. Some Integrals Involving Spherical Harmonics 148
5.10. Sums Involving Spherical Harmonics • 150
5.11. Generating Functions for Yim{d, p) 151
5.12. Asymptotic Expressions for Yim(d, p) 152
5.13. Yim(ö, p) for Special Values of l and m 155
5.14. Yjm(#, p) and for Special t? 158
5.15. Zeros of Yltn{#, p) and (d/d0)Yjm(0, tp) 158
5.16. Bipolar and Tripolar Spherical Harmonics 160
5.17. Expansions of Functions Which Depend on Two Vectors 163
Chapter 6. Spin Functions 170
6.1. Spin Functions of Particles with Arbitrary Spin 170
6.2. Spin Functions for S = | 178
6.3. Spin Functions for S = 1 185
Chapter 7. Tensor Spherical Harmonics 196
7.1. General Properties of Tensor Spherical Harmonics 196
7.2. Spinor Spherical Harmonics 202
7.3. Vector Spherical Harmonics 208
7.4. Other Notations for Tensor Spherical Harmonics 234
Contents ix
Chapter 8. Clebsch-Gordan Coefficients and 3jm Symbols 235
8.1. Definition 235
8.2. Explicit Forms of the Clebsch-Gordan Coefficients and
Their Relations to Other Functions 237
8.3. Integral Representations 243
8.4. Symmetry Properties 244
8.5. Explicit Forms of the Clebsch-Gordan Coefficients for
Special Values of the Arguments 248
8.6. Recursion Relations for the Clebsch-Gordan Coefficients 252
8.7. Sums of Products of the Clebsch-Gordan Coefficients 259
8.8. Generating Functions 263
8.9. Classical Limit and Asymptotic Expressions for the Clebsch-Gordan Coefficients . 264
8.10. Zeros of the Vector-Addition Coefficients 268
8.11. Connection of the Clebsch-Gordan Coefficients and
the 3 jm Symbols with Analogous Functions of Other Authors 268
8.12. Algebraic Tables of the Clebsch-Gordan Coefficients 270
8.13. Numerical Tables of the Clebsch-Gordan Coefficients 270
Chapter 9. 6j Symbols and the Racah Coefflcients 290
9.1. Definition 290
9.2. General Expressions for the 6j Symbols.
Relations Between the 6j Symbols and Other Functions 293
9.3. Integral Representations of the 6j Symbols 297
9.4. Symmetries of the 6j Symbols and the Racah Coefficients 298
9.5. Explicit Forms of the 6/ Symbols for Certain Arguments 299
9.6. Recursion Relations 303
9.7. Generating Function 305
9.8. Sums Involving the 6j Symbols 305
9.9. Asymptotics of the 6j Symbols for Large Angular Momenta 306
9.10. Relations Between the Wigner 6j Symbols and Analogous Functions of
Other Authors 310
9.11. Tables of Algebraic Expressions for the 6j Symbols 310
9.12. Numerical Values of the 6j Symbols 310
Chapter 10. 9j and 12j Symbols 333
10.1. Definition of the 9/ Symbols 333
10.2. Explicit Forms of the 9j Symbols and Their Relations to Other Functions . . . 336
10.3. Integral Representations of the 9 j Symbols 340
10.4. Symmetry Properties of the 9j Symbols 342
10.5. Recursion Relations for the 9j Symbols 345
10.6. Generating Function of the 9/ Symbols 351
10.7. Asymptotic Expression for a 9j Symbol 351
10.8. Explicit Forms of the 9j Symbols at Some Relations Between Arguments .... 352
10.9. Explicit Forms of the 9j Symbols for Special Values of the Arguments 357
X
Contents
10.10. Relations Between the Wigner 9j Symbols and Analogous Functions of
Other Authors 359
10.11. Tables of Algebraic Formulas of the 9j Symbols 359
10.12. Tables of Numerical Values of the 9j Symbols 360
10.13. 12j Symbols 361
Chapter 11. The Graphical Method in Angular Momentum Theory 412
11.1. Graphical Representation of Functions 412
11.2. Graphical Representation of the Main Operations of the Theory 419
11.3. Rules of the Graphical Technique 424
11.4. Summary of the Graphical Technique 446
Chapter 12. Sums Involving Vector Addition and Recoupling Coefficients 452
12.1. Summation of Products of 3jm Symbols 452
12.2. Summation of Products of 6j and 9j Symbols 462
Chapter 13. Matrix Elements of Irreducible Tensor Operators 475
13.1. The Wigner-Eckart Theorem and the Evaluation of Matrix Elements 475
13.2. Matrix Elements of Basic Tensor Operators 483
Glossary of Symbols and Notation 505
References 509
|
| any_adam_object | 1 |
| author | Varšalovič, Dimitrij A. Moskalev, A. N. Chersonskij, Valerij K. |
| author_facet | Varšalovič, Dimitrij A. Moskalev, A. N. Chersonskij, Valerij K. |
| author_role | aut aut aut |
| author_sort | Varšalovič, Dimitrij A. |
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| building | Verbundindex |
| bvnumber | BV013379234 |
| classification_rvk | UK 3500 |
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| discipline | Physik |
| edition | 1. reprint |
| format | Book |
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| id | DE-604.BV013379234 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:44:48Z |
| institution | BVB |
| isbn | 9971501074 9971509962 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009126015 |
| oclc_num | 256192092 |
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| owner_facet | DE-19 DE-BY-UBM DE-703 DE-188 |
| physical | X, 514 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Varšalovič, Dimitrij A. Verfasser aut Kvantovaja teorija uglovogo momenta Quantum theory of angular momentum irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols D. A. Varshalovich ; A. N. Moskalev ; V. K. Khersonskii 1. reprint Singapore [u.a.] World Scientific 1989 X, 514 S. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Drehimpuls (DE-588)4150572-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Drehimpuls (DE-588)4150572-4 s Quantenmechanik (DE-588)4047989-4 s DE-604 Moskalev, A. N. Verfasser aut Chersonskij, Valerij K. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009126015&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Varšalovič, Dimitrij A. Moskalev, A. N. Chersonskij, Valerij K. Quantum theory of angular momentum irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols Drehimpuls (DE-588)4150572-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4150572-4 (DE-588)4047989-4 |
| title | Quantum theory of angular momentum irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols |
| title_alt | Kvantovaja teorija uglovogo momenta |
| title_auth | Quantum theory of angular momentum irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols |
| title_exact_search | Quantum theory of angular momentum irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols |
| title_full | Quantum theory of angular momentum irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols D. A. Varshalovich ; A. N. Moskalev ; V. K. Khersonskii |
| title_fullStr | Quantum theory of angular momentum irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols D. A. Varshalovich ; A. N. Moskalev ; V. K. Khersonskii |
| title_full_unstemmed | Quantum theory of angular momentum irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols D. A. Varshalovich ; A. N. Moskalev ; V. K. Khersonskii |
| title_short | Quantum theory of angular momentum |
| title_sort | quantum theory of angular momentum irreducible tensors spherical harmonics vector coupling coefficients 3nj symbols |
| title_sub | irreducible tensors, spherical harmonics, vector coupling coefficients, 3nj symbols |
| topic | Drehimpuls (DE-588)4150572-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Drehimpuls Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009126015&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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