Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2009 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2009
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149157 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics / A.A. Andrianov, A.V. Sokolov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 42 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862653397328461824 |
|---|---|
| author | Andrianov, A.A. Sokolov, A.V. |
| author_facet | Andrianov, A.A. Sokolov, A.V. |
| citation_txt | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics / A.A. Andrianov, A.V. Sokolov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 42 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.
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| first_indexed | 2025-12-01T23:12:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149157 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T23:12:59Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Andrianov, A.A. Sokolov, A.V. 2019-02-19T17:49:49Z 2019-02-19T17:49:49Z 2009 Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics / A.A. Andrianov, A.V. Sokolov // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 42 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81Q60; 81R15; 47B15 https://nasplib.isofts.kiev.ua/handle/123456789/149157 When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples. This paper is a contribution to the Proceedings of the VIIth Workshop “Quantum Physics with NonHermitian Operators” (June 29 – July 11, 2008, Benasque, Spain). This work was partially supported by Grant RFBR 09-01-00145-a and Program RNP2009-1575. The work of A.A. was also supported by grants 2005SGR00564, 2009SGR, FPA200-66665 and by the Consolider-Ingenio 2010 Program CPAN (CSD2007-00042). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics Article published earlier |
| spellingShingle | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics Andrianov, A.A. Sokolov, A.V. |
| title | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_full | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_fullStr | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_full_unstemmed | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_short | Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics |
| title_sort | hidden symmetry from supersymmetry in one-dimensional quantum mechanics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149157 |
| work_keys_str_mv | AT andrianovaa hiddensymmetryfromsupersymmetryinonedimensionalquantummechanics AT sokolovav hiddensymmetryfromsupersymmetryinonedimensionalquantummechanics |