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dc.contributor.authorKalnins, Ernie G.en_NZ
dc.contributor.authorMiller, W., Jr.en_NZ
dc.date.accessioned2016-07-22T01:58:24Z
dc.date.available2014en_NZ
dc.date.available2016-07-22T01:58:24Z
dc.date.issued2014en_NZ
dc.identifier.citationKalnins, E. G., & Miller, W., Jr. (2014). Quadratic algebra contractions and second-order superintegrable systems. Analysis and Applications, 12(5), 583–612. http://doi.org/10.1142/S0219530514500377en
dc.identifier.issn0219-5305en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/10554
dc.description.abstractQuadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of second-order superintegrable systems in two dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces, we show that the free quadratic algebras generated by the first- and second-order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials. © 2014 World Scientific Publishing Company.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.rightsThis is an author’s accepted version of an article published in the journal: Analysis and Applications. © 2014 World Scientific Publishing Company.
dc.titleQuadratic algebra contractions and second-order superintegrable systemsen_NZ
dc.typeJournal Article
dc.identifier.doi10.1142/S0219530514500377en_NZ
dc.relation.isPartOfAnalysis and Applicationsen_NZ
pubs.begin-page583
pubs.elements-id85356
pubs.end-page612
pubs.issue5en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume12en_NZ
dc.identifier.eissn1793-6861en_NZ


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