  The Schrodinger equation for stationary states is studied in a central
potential V(r) proportional to the inverse power of r of degree beta in an
arbitrary number of spatial dimensions. The presence of a single term in the
potential makes it impossible to use previous algorithms, which only work for
quasi-exactly-solvable problems. Nevertheless, the analysis of the stationary
Schrodinger equation in the neighbourhood of the origin and of the point at
infinity is found to provide relevant information about the desired solutions
for all values of the radial coordinate. The original eigenvalue equation is
mapped into a differential equation with milder singularities, and the role
played by the particular case beta=4 is elucidated. In general, whenever the
parameter beta is even and larger than 4, a recursive algorithm for the
evaluation of eigenfunctions is obtained. Eventually, in the particular case of
two spatial dimensions, the exact form of the ground-state wave function is
obtained for a potential containing a finite number of inverse powers of r,
with the associated energy eigenvalue.
