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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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146804 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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dspace |
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irk-123456789-1468042019-02-12T01:24:28Z Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions Quesne, C. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146804 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 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. |
| format |
Article |
| author |
Quesne, C. |
| spellingShingle |
Quesne, C. Revisiting the Symmetries of the Quantum Smorodinsky-Winternitz System in D Dimensions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Quesne, C. |
| author_sort |
Quesne, C. |
| title |
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_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_sort |
revisiting the symmetries of the quantum smorodinsky-winternitz system in d dimensions |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146804 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT quesnec revisitingthesymmetriesofthequantumsmorodinskywinternitzsysteminddimensions |
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2023-05-20T17:25:51Z |
| last_indexed |
2023-05-20T17:25:51Z |
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1796153275995652096 |