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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2009
Hauptverfasser: Calzada, J.A., Negro, J., del Olmo, M.A.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2009
Online Zugang:https://nasplib.isofts.kiev.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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-149167
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).
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Intertwining Symmetry Algebras of Quantum Superintegrable Systems
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Intertwining Symmetry Algebras of Quantum Superintegrable Systems
spellingShingle Intertwining Symmetry Algebras of Quantum Superintegrable Systems
Calzada, J.A.
Negro, J.
del Olmo, M.A.
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
author Calzada, J.A.
Negro, J.
del Olmo, M.A.
author_facet Calzada, J.A.
Negro, J.
del Olmo, M.A.
publishDate 2009
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
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AT negroj intertwiningsymmetryalgebrasofquantumsuperintegrablesystems
AT delolmoma intertwiningsymmetryalgebrasofquantumsuperintegrablesystems
first_indexed 2025-11-30T16:09:55Z
last_indexed 2025-11-30T16:09:55Z
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