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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorPost, Sarah
dc.date.accessioned2008-12-09T22:38:33Z
dc.date.available2008-12-09T22:38:33Z
dc.date.issued2008-01
dc.identifier.citationKalnins, E. G., Miller, W., Jr. & Post, S. (2008). Models for quadratic algebras associated with second order superintegrable systems in 2D. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 4, 1- 21.en_US
dc.identifier.urihttps://hdl.handle.net/10289/1566
dc.description.abstractThere are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible representations of the quantum quadratic algebras though the construction of models in which the symmetries act on spaces of functions of a single complex variable via either differential operators or difference operators. In another paper we have already carried out parts of this analysis for the generic nondegenerate superintegrable system on the complex 2-sphere. Here we carry it out for a degenerate superintegrable system on the 2-sphere. We point out the connection between our results and a position dependent mass Hamiltonian studied by Quesne. We also show how to derive simple models of the classical quadratic algebras for superintegrable systems and then obtain the quantum models from the classical models, even though the classical and quantum quadratic algebras are distinct.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherSIGMAen_NZ
dc.relation.urihttp://www.imath.kiev.ua/~sigma/2008/008/en_US
dc.rightsThis article has been published in the journal: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). Used with permission.en_US
dc.subjectsuperintegrabilityen_US
dc.subjectquadratic algebrasen_US
dc.subjectWilson polynomialsen_US
dc.titleModels for quadratic algebras associated with second order superintegrable systems in 2Den_US
dc.typeJournal Articleen_US
dc.identifier.doi10.3842/SIGMA.2008.008en_US
dc.relation.isPartOfSymmetry, Integrability and Geometry: Methods and Applicationsen_NZ
pubs.begin-page1en_NZ
pubs.elements-id33416
pubs.end-page21en_NZ
pubs.volume4en_NZ


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