RT Journal Article
T1 Quasi-exact solvability in a general polynomial setting
A1 Gómez-Ullate Otaiza, David
A1 Kamran, Niky
A1 Milson, Robert
AB 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.
PB IOP Publishing
SN 0266-5611
YR 2007
FD 2007-10
LK https://hdl.handle.net/20.500.14352/51449
UL https://hdl.handle.net/20.500.14352/51449
LA eng
NO © 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
NO Ramón y Cajal program of the Ministerio de Ciencia y Tecnología
NO DGI
NO NSERC
DS Docta Complutense
RD 7 jun 2025