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

N. Debergh
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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.

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N. Debergh. 2000-05-16. On the relation between polynomial deformations of sl(2,R) and quasi-exactly solvability. https://doi.org/10.1088/0305-4470%2F33%2F40%2F308

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