2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185461A 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, LateXHigh Energy Physics - Theorytext