New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance

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dc.creatorCannata, F.
dc.creatorIoffe, M. V.
dc.creatorNishnianidze, D. N.
dc.date2002-01-13
dc.date.accessioned2026-07-07T10:53:44Z
dc.date.available2026-07-07T10:53:44Z
dc.descriptionTwo new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations of Higher order SUSY Quantum Mechanics (HSUSY QM) with supercharges allowing for separation of variables. 2)The second one is a generalization of shape invariance. While in one dimension shape invariance allows to solve algebraically a class of (exactly solvable) quantum problems, its generalization to higher dimensions has not been yet explored. Here we provide a formal framework in HSUSY QM for two-dimensional quantum mechanical systems for which shape invariance holds. Given the knowledge of one eigenvalue and eigenfunction, shape invariance allows to construct a chain of new eigenfunctions and eigenvalues. These methods are applied to a two-dimensional quantum system, and partial explicit solvability is achieved in the sense that only part of the spectrum is found analytically and a limited set of eigenfunctions is constructed explicitly.
dc.description25 pages, Latex, Journal of Physics A, to be published
dc.identifierhttps://arxiv.org/abs/hep-th/0201080
dc.identifierhttp://arxiv.org/abs/hep-th/0201080
dc.identifierJ.Phys.A35:1389-1404,2002
dc.identifierdoi:10.1088/0305-4470/35/6/305
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/185585
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.subjectQuantum Physics
dc.titleNew Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance
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