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

Shi-Hai Dong, Zhong-Qi Ma

Published 1999-01-15Version 1

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