Theory of Regge poles for 1/r2 potentials. III. An exact solution of Schrödinger’s equation for arbitrary l and E

Abstract

We give the exact solution of the radial Schrödinger equation and derive the S matrix for arbitrary energy and angular momentum for a particular 1/r2 potential with the behavior r2V (r) = −V0 at r = 0 and r2V (r) = −V2 at r = ∞. We obtain an expression for the Regge poles and study their properties and distribution at low energy. The present results are in agreement with those obtained in a previous paper in this series.