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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorPogosyan, G.S.
dc.date.accessioned2008-10-30T01:05:07Z
dc.date.available2008-10-30T01:05:07Z
dc.date.issued1996-12
dc.identifier.citationKalnins, E.G., Miller, W., Jr. & Pogosyan, G.S. (1996). Superintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensions. Journal of Mathematical Physics, 37, 6439.en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1201
dc.description.abstractIn this work we examine the basis functions for those classical and quantum mechanical systems in two dimensions which admit separation of variables in at least two coordinate systems. We do this for the corresponding systems defined in Euclidean space and on the two-dimensional sphere. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup Cartesian and polar coordinate cases, and the details of the structure of the quadratic algebras. We also study the polynomial eigenfunctions in elliptic coordinates of the n-dimensional isotropic quantum oscillator.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/37/6439/1en_US
dc.rightsCopyright 1996 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspen_US
dc.subjectMathematicsen_US
dc.subjectgroup theoryen_US
dc.subjecteuclidean spaceen_US
dc.subjectspheresen_US
dc.subjectpolynomialsen_US
dc.subjectcoordinatesen_US
dc.subjectpotential energyen_US
dc.subjectHamiltoniansen_US
dc.subjecteigenfunctionsen_US
dc.subjectsymmetry groupsen_US
dc.subjectoscillatorsen_US
dc.titleSuperintegrability and associated polynomial solutions: Euclidean space and the sphere in two dimensionsen_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1063/1.531786en_US
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
pubs.begin-page6439en_NZ
pubs.elements-id84069
pubs.end-page6467en_NZ
pubs.issue12en_NZ
pubs.volume37en_NZ


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