info:eu-repo/semantics/article
An ubiquitous three-term recurrence relation
Fecha
2021-03Registro en:
Amore, Paolo; Fernández, Francisco Marcelo; An ubiquitous three-term recurrence relation; American Institute of Physics; Journal of Mathematical Physics; 62; 3; 3-2021; 1-7
0022-2488
CONICET Digital
CONICET
Autor
Amore, Paolo
Fernández, Francisco Marcelo
Resumen
We solve an eigenvalue equation that appears in several papers about a wide range of physical problems. The Frobenius method leads to a three-term recurrence relation for the coefficients of the power series that, under suitable truncation, yields exact analytical eigenvalues and eigenfunctions for particular values of a model parameter. From these solutions, some researchers have derived a variety of predictions such as allowed angular frequencies, allowed field intensities, and the like. We also solve the eigenvalue equation numerically by means of the variational Rayleigh-Ritz method and compare the resulting eigenvalues with those provided by the truncation condition. In this way, we prove that those physical predictions are merely artifacts of the truncation condition.