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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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2009
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/149167 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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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irk-123456789-1491672019-02-20T01:27:12Z Intertwining Symmetry Algebras of Quantum Superintegrable Systems Calzada, J.A. Negro, J. del Olmo, M.A. 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. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149167 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 |
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. |
| format |
Article |
| author |
Calzada, J.A. Negro, J. del Olmo, M.A. |
| spellingShingle |
Calzada, J.A. Negro, J. del Olmo, M.A. Intertwining Symmetry Algebras of Quantum Superintegrable Systems Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Calzada, J.A. Negro, J. del Olmo, M.A. |
| author_sort |
Calzada, J.A. |
| title |
Intertwining Symmetry Algebras of Quantum Superintegrable Systems |
| title_short |
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_sort |
intertwining symmetry algebras of quantum superintegrable systems |
| publisher |
Інститут математики НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149167 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT calzadaja intertwiningsymmetryalgebrasofquantumsuperintegrablesystems AT negroj intertwiningsymmetryalgebrasofquantumsuperintegrablesystems AT delolmoma intertwiningsymmetryalgebrasofquantumsuperintegrablesystems |
| first_indexed |
2025-07-12T21:33:10Z |
| last_indexed |
2025-07-12T21:33:10Z |
| _version_ |
1837478435215114240 |