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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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2007
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/147217 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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irk-123456789-1472172019-02-14T01:25:24Z Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force González León, M.A. Mateos Guilarte, J. M. de la Torre Mayado 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147217 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
González León, M.A. Mateos Guilarte, J. M. de la Torre Mayado |
| spellingShingle |
González León, M.A. Mateos Guilarte, J. M. de la Torre Mayado Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
González León, M.A. Mateos Guilarte, J. M. de la Torre Mayado |
| author_sort |
González León, M.A. |
| title |
Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force |
| title_short |
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_sort |
two-dimensional supersymmetric quantum mechanics: two fixed centers of force |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147217 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-11T01:38:45Z |
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2025-07-11T01:38:45Z |
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