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

Abstract

Making use of an ${\it ansatz}$ for the eigenfunctions, we obtain an exact closed form solution to the non-relativistic Schr\"{o}dinger 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.