Schrödinger Equation with the Potential $V(r)=a{r}^2+b{r}^{-4}+c{r}^{-6}$

Abstract

By making use of an $ansatz$ for the eigenfunction, we obtain the exact solutions to the Schrödinger equation with the anharmonic potential, $V(r)=a{r}^2+b{r}^{-4}+c{r}^{-6}$, both in three dimensions and in two dimensions, where the parameters $a$, $b$, and $c$ in the potential satisfy some constraints.

PS file 10 pages, Submitted to J.P.A