New quasi-exactly solvable Hamiltonians in two dimensions | Zendy

Artemio González-López | Zendy; Niky Kamran | Zendy; Peter J. Olver | Zendy

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New quasi-exactly solvable Hamiltonians in two dimensions

Author(s) -

Artemio González-López,

Niky Kamran,

Peter J. Olver

Publication year - 1994

Publication title -

communications in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.662

H-Index - 152

eISSN - 1432-0916

pISSN - 0010-3616

DOI - 10.1007/bf02099982

Subject(s) - mathematics , lie algebra , algebra over a field , variety (cybernetics) , pure mathematics , differential operator , universal enveloping algebra , spectrum (functional analysis) , lie conformal algebra , algebraic number , order (exchange) , graded lie algebra , mathematical analysis , physics , quantum mechanics , statistics , finance , economics

Quasi-exactly solvable Schrodinger 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

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