An asymptotic series solution to the Schroedinger equation for a model potential

Using the method of Frobenius, the attempt to find a closed-form solution to the Schroedinger equation for a model potential V(r)=-Ze2/√(r2+a2) is described. Inspection of the series solution in the asymptotic region suggests a substitution of a four term recurrence relation by a two term relation in order to extract explicit solutions that approach to those obtained for the hydrogen atom as a→0 smoothly. The resulting approximate solutions are compared with numerical ones and shown to provide a good basis set for high Rydberg states. (orig.)