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Quasi-exactly solvable Schrödinger operators in three dimensions. (English) Zbl 1136.81038

Summary: 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.

MSC:

81U15 Exactly and quasi-solvable systems arising in quantum theory
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
22E70 Applications of Lie groups to the sciences; explicit representations
53C80 Applications of global differential geometry to the sciences
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