Real Lie algebras of differential operators and quasi-exactly solvable potentials
- 15 May 1996
- journal article
- research article
- Published by The Royal Society in Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Vol. 354 (1710) , 1165-1193
- https://doi.org/10.1098/rsta.1996.0044
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, ave 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 Schrodinger operators on R(2).All Related Versions
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