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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorKress, Jonathan M.
dc.contributor.authorMiller, W., Jr.
dc.date.accessioned2009-01-15T23:19:32Z
dc.date.available2009-01-15T23:19:32Z
dc.date.issued2007
dc.identifier.citationKalnins, E G, Kress, J M & Miller, W. J.(2007). Nondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varieties. Journal of Mathematical Physics, 48(11), 1-26.en
dc.identifier.urihttps://hdl.handle.net/10289/1791
dc.description.abstractA classical (or quantum) second order superintegrable system is an integrable n-dimensional Hamiltonian system with potential that admits 2n−1 functionally independent second order constants of the motion polynomial in the momenta, the maximum possible. Such systems have remarkable properties: multi-integrability and multiseparability, an algebra of higher order symmetries whose representation theory yields spectral information about the Schrödinger operator, deep connections with special functions, and with quasiexactly solvable systems. Here, we announce a complete classification of nondegenerate (i.e., four-parameter) potentials for complex Euclidean 3-space. We characterize the possible superintegrable systems as points on an algebraic variety in ten variables subject to six quadratic polynomial constraints. The Euclidean group acts on the variety such that two points determine the same superintegrable system if and only if they lie on the same leaf of the foliation. There are exactly ten nondegenerate potentials. ©2007 American Institute of Physicsen
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherAmerican Institute of Physicsen
dc.relation.urihttp://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JMAPAQ000048000011113518000001&idtype=cvips&gifs=yesen
dc.rightsThis article has been published in Journal of Mathematical Physics. ©2007 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.en
dc.subjectmathematicsen
dc.subjectdifferential algebraic equationsen
dc.subjectpolynomial approximationen
dc.subjectSchrodinger equationen
dc.titleNondegenerate three-dimensional complex Euclidean superintegrable systems and algebraic varietiesen
dc.typeJournal Articleen
dc.identifier.doi10.1063/1.2817821en
dc.relation.isPartOfJournal of Mathematical Physicsen_NZ
pubs.begin-page113518en_NZ
pubs.elements-id32718
pubs.end-page113518en_NZ
pubs.issue11en_NZ
pubs.volume48en_NZ
uow.identifier.article-noARTN 113518en_NZ


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