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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.

Item Type: | Article |
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Additional Information: | © IOP Publishing. |

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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