CONICET | Buscador de Institutos y Recursos Humanos

We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to athree-term recurrence relation for the coeffiients of the power series that, under suitable truncation, yields exact analytical eigenvalues andeigenfunctions for particular values of a model parameter. From these solutions, some researchers have derived a variety of predictions suchas allowed angular frequencies, allowed fild intensities, and the like. We also solve the eigenvalue equation numerically by means of thevariational Rayleigh?Ritz method and compare the resulting eigenvalues with those provided by the truncation condition. In this way, weprove that those physical predictions are merely artifacts of the truncation condition.