RT Journal Article
T1 Quasi-exact solvability and the direct approach to invariant subspaces
A1 Gómez-Ullate Otaiza, David
A1 Kamran, Niky
A1 Milson, Robert
AB We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: we show that the generalized Lame potential possesses four algebraic sectors, and describe a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.
PB IOP science
SN 0305-4470
YR 2005
FD 2005-03-04
LK https://hdl.handle.net/20.500.14352/51461
UL https://hdl.handle.net/20.500.14352/51461
LA eng
NO ©IOP science.The research of DGU is supported in part by a CRM-ISM Postdoctoral Fellowship and the Spanish Ministry of Education under grant EX2002-0176. The research of NK and RM is supported by the National Science and Engineering Research Council of Canada. DGU would like to thank the Department of Mathematics and Statistics of  alhousie University for their warm hospitality.
NO Spanish Ministry of Education
NO National Science and Engineering Research Council of Canada
DS Docta Complutense
RD 13 abr 2025