We consider the eigenvalue problem for the radial Schrödinger equation with potentials of the form $V\left(r\right)=S\left(r\right)/r+R\left(r\right)\mathrm{}$ where $S\left(r\right)\mathrm{}$ and $R\left(r\right)\mathrm{}$ are well behaved functions which tend to some (not necessarily equal) constants when $\overrightarrow{r}0$ and $\overrightarrow{r}\infty .$ Formulas (14.4.5)–(14.4.8) of Abramowitz and Stegun [Handbook of Mathematical Functions, 8th ed. (Dover, New York, 1972)], corresponding to the pure Coulomb case, are here generalized for this distorted case. We also present a complete procedure for the numerical solution of the problem. Our procedure is robust, very economic and particularly suited for very large n. Numerical illustrations for n up to 2000 are given.

• Received 11 May 1999

DOI:https://doi.org/10.1103/PhysRevE.61.3151