Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force
The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2007 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147217 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force / M.A. González León, J. Mateos Guilarte, // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 45 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862652238353137664 |
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| author | González León, M.A. Mateos Guilarte, J. M. de la Torre Mayado |
| author_facet | González León, M.A. Mateos Guilarte, J. M. de la Torre Mayado |
| citation_txt | Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force / M.A. González León, J. Mateos Guilarte, // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 45 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states.
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| first_indexed | 2025-12-01T20:40:49Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147217 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T20:40:49Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | González León, M.A. Mateos Guilarte, J. M. de la Torre Mayado 2019-02-13T19:14:22Z 2019-02-13T19:14:22Z 2007 Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force / M.A. González León, J. Mateos Guilarte, // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 45 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81Q60; 81V55 https://nasplib.isofts.kiev.ua/handle/123456789/147217 The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). We are grateful to Mikhail Iof fe for many enlightening lessons and conversations on SUSY quantum mechanics as well as letting us know about reference [28]. JMG thanks Nigel Hitchin for sending him his unpublished lecture notes on the Dirac operator. Finally, we recognize financial support from the Spanish DGICYT and the Junta de Castilla y Le´on under contracts: FIS2006-09417, VAO13C05. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force Article published earlier |
| spellingShingle | Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force González León, M.A. Mateos Guilarte, J. M. de la Torre Mayado |
| title | Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force |
| title_full | Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force |
| title_fullStr | Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force |
| title_full_unstemmed | Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force |
| title_short | Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force |
| title_sort | two-dimensional supersymmetric quantum mechanics: two fixed centers of force |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147217 |
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