Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials

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dc.creatorMarquette, Ian
dc.date2008-07-17
dc.date2009-01-06
dc.date.accessioned2026-07-07T12:39:07Z
dc.date.available2026-07-07T12:39:07Z
dc.descriptionWe consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in Cartesian coordinates with a third order integral are known. The general formalism is applied to quantum reducible and irreducible rational potentials separable in Cartesian coordinates in E2. We also discuss these potentials from the point of view of supersymmetric and PT-symmetric quantum mechanics.
dc.description33 pages, references added, misprints corrected
dc.identifierhttps://arxiv.org/abs/0807.2858
dc.identifierhttp://arxiv.org/abs/0807.2858
dc.identifierJ.Math.Phys.50:012101,2009
dc.identifierdoi:10.1063/1.3013804
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219000
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subject81R05
dc.titleSuperintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials
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