Scattering by the Singular Potential r−4

Abstract

The potential 1/r⁴ is the only known potential more singular than the centrifugal term, for which the Schrödinger equation can be solved exactly. In the present investigation, we consider the potential in more detail than has been done so far. In particular the physical S‐matrix is obtained, shown to be unitary, and compared with expressions of other derivations given in the literature. The eigenvalues of the Mathieu equation are finally discussed, and the behavior of the Regge trajectories is indicated.