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Quasi-exact solvability in a general polynomial setting

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Gómez-Ullate Otaiza, David and Kamran, Niky and Milson, Robert (2007) Quasi-exact solvability in a general polynomial setting. Inverse problems, 23 (5). pp. 1915-1942. ISSN 0266-5611

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Official URL: http://dx.doi.org/10.1088/0266-5611/23/5/008




Abstract

Our goal in this paper is to extend the theory of quasi-exactly solvable Schrodinger operators beyond the Lie-algebraic class. Let P-n be the space of nth degree polynomials in one variable. We first analyze exceptional polynomial subspaces M subset of P-n, which are those proper subspaces of Pn invariant under second-order differential operators which do not preserve Pn. We characterize the only possible exceptional subspaces of codimension one and we describe the space of second-order differential operators that leave these subspaces invariant. We then use equivalence under changes of variable and gauge transformations to achieve a complete classification of these new, non-Lie algebraic Schrodinger operators. As an example, we discuss a finite gap elliptic potential which does not belong to the Treibich-Verdier class.


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© IOP Publishing.
The research of DGU is supported in part by the Ramón y Cajal program of the Ministerio de Ciencia y Tecnología and by the DGI under grants FIS2005-00752 and MTM2006-00478. The research of NK and RM is supported in part by the NSERC grants RGPIN 105490-2004 and RGPIN-228057-2004, respectively

Uncontrolled Keywords:Solvable schrodinger-operators; Tangential covers; Calogero; Potentials; Monomials; Equations; Algebras; Spaces
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30841
Deposited On:15 Jun 2015 09:22
Last Modified:10 Dec 2018 15:09

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