Gross misinterpretation of a conditionally solvable eigenvalue equation

Abstract

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 like 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.

arXiv admin note: text overlap with arXiv:2009.07039, arXiv:2008.03376

References in corpus (5)

• On the Klein-Gordon oscillator subject to a Coulomb-type potential
• On the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects on the Harmonic Oscillator
• Bound states for a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field
• Threading dislocation densities in semiconductor crystals: a geometric approach
• Comment on: "Interaction of the magnetic quadrupole moment of a non-relativistic particle with an electric field in a rotating frame. Ann. Phys. 412 (2020) 168040''