Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions
The D-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known symmetry and dynamical algebras. The first two are obtained in hyp...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2011 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2011
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146804 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 90 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710963621330944 |
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| author | Quesne, C. |
| author_facet | Quesne, C. |
| citation_txt | Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 90 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The D-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known symmetry and dynamical algebras. The first two are obtained in hyperspherical coordinates by introducing D auxiliary continuous variables and by reducing a 2D-dimensional harmonic oscillator Hamiltonian. The su(2D) symmetry and w(2D)⊕s sp(4D,R) dynamical algebras of this Hamiltonian are then transformed into the searched for potential and dynamical potential algebras of the Smorodinsky-Winternitz system. The action of generators on wavefunctions is given in explicit form for D=2.
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| first_indexed | 2025-12-07T17:27:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146804 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:27:47Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Quesne, C. 2019-02-11T15:30:54Z 2019-02-11T15:30:54Z 2011 Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions / C. Quesne // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 90 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20C35; 81R05; 81R12 DOI:10.3842/SIGMA.2011.035 https://nasplib.isofts.kiev.ua/handle/123456789/146804 The D-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known symmetry and dynamical algebras. The first two are obtained in hyperspherical coordinates by introducing D auxiliary continuous variables and by reducing a 2D-dimensional harmonic oscillator Hamiltonian. The su(2D) symmetry and w(2D)⊕s sp(4D,R) dynamical algebras of this Hamiltonian are then transformed into the searched for potential and dynamical potential algebras of the Smorodinsky-Winternitz system. The action of generators on wavefunctions is given in explicit form for D=2. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions Article published earlier |
| spellingShingle | Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions Quesne, C. |
| title | Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions |
| title_full | Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions |
| title_fullStr | Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions |
| title_full_unstemmed | Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions |
| title_short | Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions |
| title_sort | revisiting the symmetries of the quantum smorodinsky-winternitz system in d dimensions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146804 |
| work_keys_str_mv | AT quesnec revisitingthesymmetriesofthequantumsmorodinskywinternitzsysteminddimensions |