Discrete Sturm-Liouville operators having the hydrogen atom potential

Abstract

In the present paper, we investigate Sturm-Liouville difference operators having $\frac{2}{n}-\frac{r(r+1)}{n^2}$ type singularity. We study the properties of the eigenvalues of discrete boundary value problem and present the eigenfunction expansion. Finally, we show that the potential can be uniquely determined by the eigenvalues and weight numbers, and some numerical results are given to illustrate the main findings.