An ubiquitous three-term recurrence relation

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