  We use the Tridiagonal Representation Approach (TRA) to obtain exact bound
states solution (energy spectrum and wavefunction) of the Schr\"odinger
equation for a three-parameter short-range potential with 1/r, 1/r^2 and 1/r^3
singularities at the origin. The solution is a finite series of square
integrable functions with weighted coefficients that satisfy a three-term
recursion relation. The solution of the recursion is the discrete version of a
non-conventional orthogonal polynomial. We are currently preparing to use the
results of this work to study the binding of an electron to a molecule with an
effective electric quadrupole moment, which has the same 1/r^3 singularity.
