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



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González López, Artemio and Kamran, Niky and Olver, Peter J. (1996) Real Lie algebras of differential operators and quasi-exactly solvable potentials. Philosophical transactions - Royal Society. Mathematical, physical and engineering science, 354 (1710). pp. 1165-1193. ISSN 1364-503X

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

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© Royal Society of London.
Acknowledgment: It is a pleasure to thank the referees for useful comments.
Supported in part by DGICYT Grant PB92-0197.
Supported in part by an NSERC Grant.
Supported in part by NSF Grants DMS 92-04192 and 95-00931.

Uncontrolled Keywords:2 Complex-variables; Quantal problems; Vector-fields
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:32868
Deposited On:26 Aug 2015 11:28
Last Modified:20 Apr 2022 12:12

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