Exact Solutions to the Schrödinger Equation for the Inverse-Power Potential in Two Dimensions

Abstract

Utilizing an $ansatz$ for the eigenfunctions, we arrive at an exact closed form solution to the Schrödinger equation with the inverse-power potential, $V(r)=a{r}^{-4}+b{r}^{-3}+c{r}^{-2}+d{r}^{-1}$ in two dimensions, where the parameters of the potential $a,b,c,d$ satisfy a constraint.

Latex file 9 pages and submit to Euro. Phys. J. D