Abstract
A very simple perturbative numerical (PN) algorithm is developed for the solution of the radial Schrödinger equation, using first order perturbation theory along the lines previously developed by Gordon. This algorithm uses the same basic approximation (a step function approximation for the potential well) as that recently reported by Riehl, Diestler, and Wagner (10). It shows, however, an O ( h 5) rate of convergence in the step size h , as compared to the O ( h 4) rate of convergence of the algorithm given in the above cited reference. In the present paper we report a new feature of the PN approach to the solution of the Schrödinger equation, namely, the remarkable stability of the present PN algorithm against the round off errors. A comparison with the Numerov method for eigenvalue problems proves the high efficiency of the present algorithm.
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