New quasi-exactly solvable Hamiltonians in two dimensions

Artemio González-López, Niky Kamran, Peter J. Olver

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Quasi-exactly solvable Schrödinger operators have the remarkable property that a part of their spectrum can be computed by algebraic methods. Such operators lie in the enveloping algebra of a finite-dimensional Lie algebra of first order differential operators-the "hidden symmetry algebra". In this paper we develop some general techniques for constructing quasi-exactly solvable operators. Our methods are applied to provide a wide variety of new explicit two-dimensional examples (on both flat and curved spaces) of quasi-exactly solvable Hamiltonians, corresponding to both semisimple and more general classes of Lie algebras.

Original languageEnglish (US)
Pages (from-to)503-537
Number of pages35
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - Jan 1994


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