The Supersymmetric Dirac equation: the application to hydrogenic atoms
Literaturverz. S. 195 - 198
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Imperial College Press
2012
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Literaturverz. S. 195 - 198 |
| Physical Description: | XIII, 201 S. graph. Darst. 23cm |
| ISBN: | 1848167970 9781848167971 |
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Record in the Search Index
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| adam_text | Titel: The supersymmetric Dirac equation
Autor: Hirshfeld, Allen
Jahr: 2012
Contents
Preface vii
List of Figures xiii
1. Introduction 1
2. The Classical Kepler Problem 5
2.1 Central Forces......................... 6
2.2 The Laplace Vector....................... 8
3. Symmetry of the Classical Problem 15
3.1 Lie Groups and Lie Algebras ................. 15
3.2 Some Special Lie Algebras .................. 18
3.3 Poisson Brackets........................ 22
3.4 The Inverse Square Law.................... 25
4. From Solar Systems to Atoms 31
4.1 Rutherford Scattering ..................... 31
4.2 Conservation of the Laplace Vector.............. 32
4.3 The Differential Cross Section................. 33
5. The Bohr Model 35
5.1 Spectroscopic Series...................... 35
5.2 The Postulates of the Model.................. 35
5.3 The Predictions of the Model ................. 37
5.4 Correction for Finite Nuclear Mass.............. 42
6. Interpretation of the Quantum Rules 47
6.1 The Sommerfeld-Wilson Quantization Conditions...... 47
6.2 de Broglie s Wave Interpretation................ 49
7. Sommerfeld s Model for Non-Relativistic Electrons 53
7.1 Assumptions of the Model................... 53
7.2 Results of the Model for Non-Relativistic
Hydrogen Atoms........................ 55
7.3 The Eccentricity........................ 57
8. Quantum Mechanics of Hydrogenic Atoms 59
8.1 Quantization.......................... 59
8.2 Quantum Mechanical Relation Between | A 2 and L2..... 61
8.3 Pauli s Hydrogenic Realization of so(4)............ 62
8.4 so(4) and the Spectrum of Hydrogenic Atoms......... 66
9. The Schrodinger Equation and the Confluent
Hypergeometric Functions 69
9.1 The Schrodinger Equation and Its Solutions.......... 69
9.2 Laguerre Polynomials and Associated
Laguerre Functions....................... 73
10. Non-Relativistic Hydrogenic Atoms with Spin 77
10.1 Spin Variables, the Pauli Hamiltonian
and Factorization........................ 77
10.2 A Theorem Concerning the Anticommutation of K...... 81
10.3 Pauli Spinors.......................... 82
10.4 Concerning the Operator ( rr) ................ 83
10.5 The Key Equation: Concerning the Operator {tr-A)..... 84
10.6 The Factorization Method................... 86
10.7 The Definition of Eccentricity................. 88
11. Elements of Supersymmetric Quantum Mechanics 91
11.1 General Considerations .................... 91
11.2 Supersymmetry of Non-Relativistic
Hydrogenic Atoms....................... 94
12. Sommerfeld s Derivation of the Relativistic Energy
Level Formula 99
12.1 Assumptions of the Model................... 100
12.2 The Energies of the Bound States............... 102
13. The Dirac Equation 105
13.1 The Hamiltonian........................ 105
13.2 Total Angular Momentum................... 107
13.3 The Dirac Operator....................... 108
13.4 A Complete Set of Mutually Commuting Operators...... 110
13.5 The Dirac Spinors....................... 111
13.6 The Radial Equations in Polar Coordinates.......... 111
14. The Primary Supersymmetry of the Dirac Equation 115
14.1 A Derivation of the Johnson-Lippmann Operator....... 115
14.2 Commutation and Anticommutation Relations
of the Johnson-Lippmann Operator.............. 119
14.3 Eccentricity........................... 120
14.4 The Johnson-Lippmann Operator as the Generator
of Supersymmetry....................... 121
15. Extending the Solution Space 127
15.1 The T-Induced Radial Supersymmetry ............ 129
15.2 The Supersymmetric Ground State
in the T Representation .................... 133
15.3 The General Solutions in the T Representation........ 134
16. A Different Extension of the Solution Space 139
16.1 The A-Induced Radial Supersymmetry............ 141
16.2 The Supersymmetric Ground State in the A Representation . 144
16.3 The General Solutions in the A Representation........ 145
17. The Relation of the Solutions to Kramer s Equation 149
17.1 The Eigenvalue Problem for Traceless
2x2 Matrices......................... 149
17.2 Eigenfunctions of the Operators T and A........... 151
17.3 Kramer s Equation....................... 154
18. Non-Relativistic Approximation 161
18.1 The T Representation ..................... 163
18.2 The A Representation..................... 164
19. Conclusions 167
Appendices 171
Appendix A. The Confluent Hypergeometric Function........ 171
Appendix B. Orthogonality Relations of Hypergeometric
Functions............................... 175
Appendix C. More Integrals Involving Hypergeometric
Functions............................... 179
Appendix D. Normalization for the IMnduced Scheme ....... 182
Appendix E. Normalization for the A-Induced Scheme....... 185
Solutions to the Exercises 189
Bibliography 195
Index 199
|
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| id | DE-604.BV040254750 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:20:05Z |
| institution | BVB |
| isbn | 1848167970 9781848167971 |
| language | English |
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| owner | DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-11 |
| physical | XIII, 201 S. graph. Darst. 23cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Hirshfeld, Allen C Verfasser aut The Supersymmetric Dirac equation the application to hydrogenic atoms Allen Hirshfeld London [u.a.] Imperial College Press 2012 XIII, 201 S. graph. Darst. 23cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 195 - 198 Dirac equation Supersymmetry Quantum field theory Supersymmetrie (DE-588)4128574-8 gnd rswk-swf Wasserstoffatom (DE-588)4189265-3 gnd rswk-swf Dirac-Gleichung (DE-588)4150116-0 gnd rswk-swf Wasserstoffatom (DE-588)4189265-3 s Dirac-Gleichung (DE-588)4150116-0 s Supersymmetrie (DE-588)4128574-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025110646&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hirshfeld, Allen C The Supersymmetric Dirac equation the application to hydrogenic atoms Dirac equation Supersymmetry Quantum field theory Supersymmetrie (DE-588)4128574-8 gnd Wasserstoffatom (DE-588)4189265-3 gnd Dirac-Gleichung (DE-588)4150116-0 gnd |
| subject_GND | (DE-588)4128574-8 (DE-588)4189265-3 (DE-588)4150116-0 |
| title | The Supersymmetric Dirac equation the application to hydrogenic atoms |
| title_auth | The Supersymmetric Dirac equation the application to hydrogenic atoms |
| title_exact_search | The Supersymmetric Dirac equation the application to hydrogenic atoms |
| title_full | The Supersymmetric Dirac equation the application to hydrogenic atoms Allen Hirshfeld |
| title_fullStr | The Supersymmetric Dirac equation the application to hydrogenic atoms Allen Hirshfeld |
| title_full_unstemmed | The Supersymmetric Dirac equation the application to hydrogenic atoms Allen Hirshfeld |
| title_short | The Supersymmetric Dirac equation |
| title_sort | the supersymmetric dirac equation the application to hydrogenic atoms |
| title_sub | the application to hydrogenic atoms |
| topic | Dirac equation Supersymmetry Quantum field theory Supersymmetrie (DE-588)4128574-8 gnd Wasserstoffatom (DE-588)4189265-3 gnd Dirac-Gleichung (DE-588)4150116-0 gnd |
| topic_facet | Dirac equation Supersymmetry Quantum field theory Supersymmetrie Wasserstoffatom Dirac-Gleichung |
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