Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 109, 24 pages      arXiv:0709.4528      http://dx.doi.org/10.3842/SIGMA.2007.109

Quasi-Exactly Solvable Schrödinger Operators in Three Dimensions

Mélisande Fortin Boisvert
Department of Mathematics and Statistics, McGill University, Montréal, Canada, H3A 2K6

Received October 01, 2007, in final form November 02, 2007; Published online November 21, 2007

Abstract
The main contribution of our paper is to give a partial classification of the quasi-exactly solvable Lie algebras of first order differential operators in three variables, and to show how this can be applied to the construction of new quasi-exactly solvable Schrödinger operators in three dimensions.

Key words: quasi-exact solvability; Schrödinger operators; Lie algebras of first order differential operators; three dimensional manifolds.

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