Intertwining Symmetry Algebras of Quantum Superintegrable Systems
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like (su(n),so(2n)) or (su(p,q),so(2p,2q)). The eigenstates of the associated Hamiltonian hierarc...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2009 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2009
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149167 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Intertwining Symmetry Algebras of Quantum Superintegrable Systems / J.A. Calzada, J. Negro, M.A. del Olmo // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 29 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862634429407559680 |
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| author | Calzada, J.A. Negro, J. del Olmo, M.A. |
| author_facet | Calzada, J.A. Negro, J. del Olmo, M.A. |
| citation_txt | Intertwining Symmetry Algebras of Quantum Superintegrable Systems / J.A. Calzada, J. Negro, M.A. del Olmo // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 29 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like (su(n),so(2n)) or (su(p,q),so(2p,2q)). The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness.
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| first_indexed | 2025-11-30T16:09:55Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149167 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-30T16:09:55Z |
| publishDate | 2009 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Calzada, J.A. Negro, J. del Olmo, M.A. 2019-02-19T17:54:19Z 2019-02-19T17:54:19Z 2009 Intertwining Symmetry Algebras of Quantum Superintegrable Systems / J.A. Calzada, J. Negro, M.A. del Olmo // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 29 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B80; 81R12; 81R15 https://nasplib.isofts.kiev.ua/handle/123456789/149167 We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like (su(n),so(2n)) or (su(p,q),so(2p,2q)). The eigenstates of the associated Hamiltonian hierarchies belong to unitary representations of these algebras. It is shown that these intertwining operators, related with separable coordinates for the system, are very useful to determine eigenvalues and eigenfunctions of the Hamiltonians in the hierarchy. An study of the corresponding superintegrable classical systems is also included for the sake of completness. 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 has been partially supported by DGES of the Ministerio de Educaci´on y Ciencia of Spain under Project FIS2005-03989 and Junta de Castilla y Le´on (Spain) (Project GR224). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Intertwining Symmetry Algebras of Quantum Superintegrable Systems Article published earlier |
| spellingShingle | Intertwining Symmetry Algebras of Quantum Superintegrable Systems Calzada, J.A. Negro, J. del Olmo, M.A. |
| title | Intertwining Symmetry Algebras of Quantum Superintegrable Systems |
| title_full | Intertwining Symmetry Algebras of Quantum Superintegrable Systems |
| title_fullStr | Intertwining Symmetry Algebras of Quantum Superintegrable Systems |
| title_full_unstemmed | Intertwining Symmetry Algebras of Quantum Superintegrable Systems |
| title_short | Intertwining Symmetry Algebras of Quantum Superintegrable Systems |
| title_sort | intertwining symmetry algebras of quantum superintegrable systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149167 |
| work_keys_str_mv | AT calzadaja intertwiningsymmetryalgebrasofquantumsuperintegrablesystems AT negroj intertwiningsymmetryalgebrasofquantumsuperintegrablesystems AT delolmoma intertwiningsymmetryalgebrasofquantumsuperintegrablesystems |