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

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

2000-05-16

arxiv.org/abs/hep-th/0005141v1

J.Phys.A33:7109-7122,2000

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LateX

Scientific paper

10.1088/0305-4470/33/40/308

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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