Convergent Iterative Solutions for a Sombrero-Shaped Potential in Any Space Dimension and Arbitrary Angular Momentum

Abstract

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with an $N$-dimensional radial potential $V=\frac{g^2}{2}(r^2-1)^2$ and an angular momentum $l$. For $g$ large, the rate of convergence is similar to a power series in $g^{-1}$.