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Intertwining Symmetry Algebras of Quantum Superintegrable Systems

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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Main Authors: Calzada, J.A., Negro, J., del Olmo, M.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2009
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/149167
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spelling 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 2023-05-20T17:32:29Z
last_indexed 2023-05-20T17:32:29Z
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