Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and shape invariance - two main ingredients of the supersymmetrical...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146511 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics / M.V. Ioffe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862670476559515648 |
|---|---|
| author | Ioffe, M.V. |
| author_facet | Ioffe, M.V. |
| citation_txt | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics / M.V. Ioffe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and shape invariance - two main ingredients of the supersymmetrical quantum mechanics. The first method explores the opportunity to separate variables in the supercharge, and it allows to find a part of spectrum of the Schrödinger Hamiltonian. The second method works when the standard separation of variables procedure can be applied for one of the partner Hamiltonians. Then the spectrum and wave functions of the second partner can be found. Both methods are illustrated by the example of two-dimensional generalization of Morse potential for different values of parameters.
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| first_indexed | 2025-12-07T15:30:51Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146511 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:30:51Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ioffe, M.V. 2019-02-09T19:39:06Z 2019-02-09T19:39:06Z 2010 Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics / M.V. Ioffe // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q60 doi:10.3842/SIGMA.2010.075 https://nasplib.isofts.kiev.ua/handle/123456789/146511 Two different approaches are formulated to analyze two-dimensional quantum models which are not amenable to standard separation of variables. Both methods are essentially based on supersymmetrical second order intertwining relations and shape invariance - two main ingredients of the supersymmetrical quantum mechanics. The first method explores the opportunity to separate variables in the supercharge, and it allows to find a part of spectrum of the Schrödinger Hamiltonian. The second method works when the standard separation of variables procedure can be applied for one of the partner Hamiltonians. Then the spectrum and wave functions of the second partner can be found. Both methods are illustrated by the example of two-dimensional generalization of Morse potential for different values of parameters. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 I am very grateful to A.A. Andrianov, F. Cannata and D.N. Nishnianidze for fruitful collaboration and many useful discussions. The work was partially supported by the RFFI grant 09-01-00145-a. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics Article published earlier |
| spellingShingle | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics Ioffe, M.V. |
| title | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics |
| title_full | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics |
| title_fullStr | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics |
| title_full_unstemmed | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics |
| title_short | Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics |
| title_sort | supersymmetrical separation of variables in two-dimensional quantum mechanics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146511 |
| work_keys_str_mv | AT ioffemv supersymmetricalseparationofvariablesintwodimensionalquantummechanics |