Acosta‑Humánez, Primitivo B.Blázquez‑Sanz, DavidVenegas‑Gómez, Henock2020-10-202020-10-202020-09-1023169028https://hdl.handle.net/20.500.12442/6724In this paper we present an algebraic study concerning the general second order linear diferential equation with polynomial coefcients. By means of Kovacic’s algorithm and asymptotic iteration method we fnd a degree independent algebraic description of the spectral set: the subset, in the parameter space, of Liouville integrable diferential equations. For each fxed degree, we prove that the spectral set is a countable union of non accumulating algebraic varieties. This algebraic description of the spectral set allow us to bound the number of eigenvalues for algebraically quasi-solvable potentials in the Schrödinger equation.pdfengAttribution-NonCommercial-NoDerivatives 4.0 InternacionalAnharmonic oscillatorsAsymptotic iteration methodKovacic algorithmLiouvillian solutionsParameter spaceQuasi-solvable modelSchrödinger equationSpectral varietiesinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://doi.org/10.1007/s40863-020-00186-0https://link.springer.com/article/10.1007/s40863-020-00186-0