Liouvillian solutions for second order linear diferential equations with polynomial coefcients

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2020-09-10

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Springer

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In 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.

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Anharmonic oscillators, Asymptotic iteration method, Kovacic algorithm, Liouvillian solutions, Parameter space, Quasi-solvable model, Schrödinger equation, Spectral varieties

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