Schrödinger equation with inverse fourth-power potential, a differential equation with two irregular singular points

Abstract

The Schrödinger radial equation with inverse fourth‐power potential is treated analytically. Solutions in the form of integral representations of the generalized Laplace type are considered. Standard solutions are defined relative to each of the two irregular singular points of the differential equation. The coefficients in the linear relations persisting between any three of the standard solutions are obtained. The expressions for the coefficients, which contain some Taylor and Laurent series and finite determinants, are suitable for electronic computation. From the coefficients the S matrix and the scattering phase shifts may be obtained immediately.