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dc.contributor.authorEscobar-Ruiz, M.A.en_NZ
dc.contributor.authorKalnins, Ernie G.en_NZ
dc.contributor.authorMiller, W., Jr.en_NZ
dc.date.accessioned2018-03-27T22:16:28Z
dc.date.available2017-09-22en_NZ
dc.date.available2018-03-27T22:16:28Z
dc.date.issued2017en_NZ
dc.identifier.citationEscobar-Ruiz, M. A., Kalnins, E. G., & Miller, W., Jr. (2017). Separation equations for 2D superintegrable systems on constant curvature spaces. Journal of Physics A: Mathematical and Theoretical, 50(38), article no. 385202. https://doi.org/10.1088/1751-8121/aa8489en
dc.identifier.issn1751-8113en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/11756
dc.description.abstractSecond-order conformal quantum superintegrable systems in two dimensions are Laplace equations on a manifold with an added scalar potential and three independent 2nd order conformal symmetry operators. They encode all the information about 2D Helmholtz or time-independent Schrödinger superintegrable systems in an efficient manner: each of these systems admits a quadratic symmetry algebra (not usually a Lie algebra) and is multiseparable. We study the separation equations for the systems as a family rather than separate cases. We show that the separation equations comprise all of the various types of hypergeometric and Heun equations in full generality. In particular, they yield all of the 1D Schrödinger exactly solvable (ES) and quasi-exactly solvable (QES) systems related to the Heun operator. We focus on complex constant curvature spaces and show explicitly that there are eight pairs of Laplace separation types and these types account for all separable coordinates on the 20 flat space and 9 2-sphere Helmholtz superintegrable systems, including those for the constant potential case. The different systems are related by Stäckel transforms, by the symmetry algebras and by Böcher contractions of the conformal algebra so(4, C) to itself, which enables all systems to be derived from a single one: the generic potential on the complex 2-sphere. This approach facilitates a unified view of special function theory, incorporating hypergeometric and Heun functions in full generality.
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherIOP Publishing Ltden_NZ
dc.rights© 2017 IOP Publishing Ltd.
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectPhysics, Multidisciplinaryen_NZ
dc.subjectPhysics, Mathematicalen_NZ
dc.subjectPhysicsen_NZ
dc.subjectsuperintegrable systemsen_NZ
dc.subjecthypergeometric equationsen_NZ
dc.subjectHeun equationsen_NZ
dc.subjectcontractionsen_NZ
dc.subjectquasiexact solvabilityen_NZ
dc.subjectEXACT SOLVABILITYen_NZ
dc.subjectEUCLIDEAN-SPACEen_NZ
dc.subjectCONTRACTIONSen_NZ
dc.subjectEXPANSIONSen_NZ
dc.subjectALGEBRAen_NZ
dc.subjectPOLYNOMIALSen_NZ
dc.subjectDIMENSIONSen_NZ
dc.subjectVARIABLESen_NZ
dc.titleSeparation equations for 2D superintegrable systems on constant curvature spacesen_NZ
dc.typeJournal Article
dc.identifier.doi10.1088/1751-8121/aa8489en_NZ
dc.relation.isPartOfJournal of Physics A: Mathematical and Theoreticalen_NZ
pubs.elements-id205803
pubs.issue38en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume50en_NZ
dc.identifier.eissn1751-8121en_NZ
uow.identifier.article-noARTN 385202


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