New quasi-exactly solvable hamiltonians in 2 dimensions



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González López, Artemio and Kamran, Niky and Olver, Peter J. (1994) New quasi-exactly solvable hamiltonians in 2 dimensions. Communications in mathematical physics, 159 (3). pp. 503-537. ISSN 0010-3616

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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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© Springer

Uncontrolled Keywords:Differential-operators; Quantum-mechanics; Partial algebraization; Lie-algebras; Scattering; Equations
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32877
Deposited On:26 Aug 2015 07:33
Last Modified:10 Dec 2018 15:10

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