A simple numerical method for singular potentials

A one-parameter family of coordinate transformations is shown to lead to a simple finite difference method which gives highly accurate energies and ex pectation values for the Schrodinger equation in which the potential consis ts of a smooth term plus a perturbing term which is singular at the origin. The method is effective down to very small values of the perturbation para meter and supplements the previously reported perturbation approach which i s valuable for large lambda values.