On the relation between polynomial deformations of sl(2,R) and quasi-exactly solvability

Abstract

A general method based on the polynomial deformations of the Lie algebra sl(2,R) is proposed in order to exhibit the quasi-exactly solvability of specific Hamiltonians implied by quantum physical models. This method using the finite-dimensional representations and differential realizations of such deformations is illustrated on the sextic oscillator as well as on the second harmonic generation.

20 pages, LateX

References in corpus (1)

• On realizations of nonlinear Lie algebras by differential operators

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