Comment on: “On the computation of eigenvalues of the anharmonic Coulombic potential”

Abstract

In this comment we show that the claims by Cassidy et al (J Math Chem 56: 477, 2018) about the limitations of the Riccati Padé method (RPM) are unfounded. To this end we compare the performance of the RPM and their DESCM by means of the calculation of the eigenvalues of a class of one-dimensional potentials. We show that the RPM is simple and extremely accurate. In addition to the exponential convergence of its approximate eigenvalues the RPM does not require any variable transformation, adjustable parameters or scaling that are necessary for the improvement of the performance of the DESCM. An additional remarkable feature of the RPM is that it provides upper and lower bounds to the eigenvalues of the perturbed Coulomb potentials chosen for this test.