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arXiv · hep-th/9604102

Real Lie Algebras of Differential Operators and Quasi-Exactly Solvable Potentials

Artemio Gonzalez-Lopez·Niky Kamran·Peter J. Olver
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Abstract

We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators in $R^2$. Furthermore, we find all algebras which are quasi-exactly solvable, along with the associated finite-dimensional modules of analytic functions. The resulting real Lie algebras are used to construct new quasi-exactly solvable Schroedinger operators on $R^2$.

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Artemio Gonzalez-Lopez, Niky Kamran, Peter J. Olver. 1996-04-17. Real Lie Algebras of Differential Operators and Quasi-Exactly Solvable Potentials. https://doi.org/10.1098/rsta.1996.0044

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