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GómezUllate Otaiza, David and Kamran, Niky and Milson, Robert (2007) Quasiexact solvability in a general polynomial setting. Inverse problems, 23 (5). pp. 19151942. ISSN 02665611

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Official URL: http://dx.doi.org/10.1088/02665611/23/5/008
URL  URL Type 

http://iopscience.iop.org  Publisher 
http://arxiv.org/abs/nlin/0610065  Organisation 
Abstract
Our goal in this paper is to extend the theory of quasiexactly solvable Schrodinger operators beyond the Liealgebraic class. Let Pn be the space of nth degree polynomials in one variable. We first analyze exceptional polynomial subspaces M subset of Pn, which are those proper subspaces of Pn invariant under secondorder differential operators which do not preserve Pn. We characterize the only possible exceptional subspaces of codimension one and we describe the space of secondorder 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, nonLie algebraic Schrodinger operators. As an example, we discuss a finite gap elliptic potential which does not belong to the TreibichVerdier class.
Item Type:  Article 

Additional Information:  © IOP Publishing. 
Uncontrolled Keywords:  Solvable schrodingeroperators; Tangential covers; Calogero; Potentials; Monomials; Equations; Algebras; Spaces 
Subjects:  Sciences > Physics > PhysicsMathematical 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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