Exact Solutions to the Schrödinger Equation for the potential $V(r)=a{r}^2+b{r}^{-4}+c{r}^{-6}$ in 2D

Abstract

Making use of an $ansatz$ for the eigenfunctions, we obtain an exact closed form solution to the non-relativistic Schrödinger equation with the anharmonic potential, $V(r)=a{r}^2+b{r}^{-4}+c{r}^{-6}$ in two dimensions, where the parameters of the potential $a,b,c$ satisfy some constraints.

arXiv commentLatex file, pages 9 and 2 eps figures, accepted by J. Phys. A

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