Real Lie algebras of differential operators and quasi-exactly solvable potentials

Artemio González-López, Niky Kamran, Peter Olver

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

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 ℝ2. 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 Schrödinger operators on ℝ2.

Original languageEnglish (US)
Pages (from-to)1165-1193
Number of pages29
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume354
Issue number1710
DOIs
StatePublished - May 15 1996

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