  In non-relativistic quantum mechanics, singular potentials in problems with
spherical symmetry lead to a Schrodinger equation for stationary states with
non-Fuchsian singularities both as r tends to zero and as r tends to infinity.
In the sixties, an analytic approach was developed for the investigation of
scattering from such potentials, with emphasis on the polydromy of the wave
function in the r variable. The present paper extends those early results to an
arbitrary number of spatial dimensions. The Hill-type equation which leads, in
principle, to the evaluation of the polydromy parameter, is obtained from the
Hill equation for a two-dimensional problem by means of a simple change of
variables. The asymptotic forms of the wave function as r tends to zero and as
r tends to infinity are also derived. The Darboux technique of intertwining
operators is then applied to obtain an algorithm that makes it possible to
solve the Schrodinger equation with a singular potential containing many
negative powers of r, if the exact solution with even just one term is already
known.
