Exact Solution of the Schrödinger Equation for Inverse Fourth-Power Potential

Abstract

The solution of the Schrödinger equation for the potential ${\mathrm{V(r)=V/(\mu r)}}^4$ and all angular momenta is given in terms of known functions, namely, the solutions to the modified Mathieu equation with complex parameters and complex argument. Scattering solutions for both attractive and repulsive potentials are given and in the latter case the explicit expression for the S matrix is given.