Models of Quadratic Algebras Generated by Superintegrable Systems in 2D
In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of Stäckel equivalent systems for both degenerate and nondegenerate systems. In almost all cases, the models can be used...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2011 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146853 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Models of Quadratic Algebras Generated by Superintegrable Systems in 2D / S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862729633190903808 |
|---|---|
| author | Post, S. |
| author_facet | Post, S. |
| citation_txt | Models of Quadratic Algebras Generated by Superintegrable Systems in 2D / S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of Stäckel equivalent systems for both degenerate and nondegenerate systems. In almost all cases, the models can be used to determine the quantization of energy and eigenvalues for integrals associated with separation of variables in the original system.
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| first_indexed | 2025-12-07T19:15:29Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146853 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:15:29Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Post, S. 2019-02-11T17:16:15Z 2019-02-11T17:16:15Z 2011 Models of Quadratic Algebras Generated by Superintegrable Systems in 2D / S. Post // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 22E70; 81R05; 17B80 DOI:10.3842/SIGMA.2011.036 https://nasplib.isofts.kiev.ua/handle/123456789/146853 In this paper, we consider operator realizations of quadratic algebras generated by second-order superintegrable systems in 2D. At least one such realization is given for each set of Stäckel equivalent systems for both degenerate and nondegenerate systems. In almost all cases, the models can be used to determine the quantization of energy and eigenvalues for integrals associated with separation of variables in the original system. This paper is a contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S⁴)”. The full collection is available at http://www.emis.de/journals/SIGMA/S4.html.
 S.P. acknowledges a postdoctoral fellowship awarded by the Laboratory of Mathematical Physics of the Centre de Recherches Math´ematiques, Universit´e de Montr´eal. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Models of Quadratic Algebras Generated by Superintegrable Systems in 2D Article published earlier |
| spellingShingle | Models of Quadratic Algebras Generated by Superintegrable Systems in 2D Post, S. |
| title | Models of Quadratic Algebras Generated by Superintegrable Systems in 2D |
| title_full | Models of Quadratic Algebras Generated by Superintegrable Systems in 2D |
| title_fullStr | Models of Quadratic Algebras Generated by Superintegrable Systems in 2D |
| title_full_unstemmed | Models of Quadratic Algebras Generated by Superintegrable Systems in 2D |
| title_short | Models of Quadratic Algebras Generated by Superintegrable Systems in 2D |
| title_sort | models of quadratic algebras generated by superintegrable systems in 2d |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146853 |
| work_keys_str_mv | AT posts modelsofquadraticalgebrasgeneratedbysuperintegrablesystemsin2d |