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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorKress, Jonathan M.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorPost, Sarah
dc.identifier.citationKalnins, E.G., Kress, J.M., Miller, W.Jr. & Post, S. (2010). Laplace-type equations as conformal superintegrable systems. Advances in Applied Mathematics, available online 27 October 2010.en_NZ
dc.description.abstractWe lay out the foundations of the theory of second order conformal superintegrable systems. Such systems are essentially Laplace equations on a manifold with an added potential: (Δn+V(x))Ψ=0. Distinct families of second order superintegrable Schrödinger (or Helmholtz) systems (Δ’n+V’(x) )Ψ=ΕΨ can be incorporated into a single Laplace equation. There is a deep connection between most of the special functions of mathematical physics, these Laplace conformally superintegrable systems and their conformal symmetry algebras. Using the theory of the Laplace systems, we show that the problem of classifying all 3D Helmholtz superintegrable systems with nondegenerate potentials, i.e., potentials with a maximal number of independent parameters, can be reduced to the problem of classifying the orbits of the nonlinear action of the conformal group on a 10-dimensional manifold.en_NZ
dc.subjectconformal superintegrabilityen_NZ
dc.subjectlaplace equationsen_NZ
dc.subjectquadratic algebrasen_NZ
dc.titleLaplace-type equations as conformal superintegrable systemsen_NZ
dc.typeJournal Articleen_NZ
dc.relation.isPartOfAdvances in Applied Mathematicsen_NZ

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