CONICET | Buscador de Institutos y Recursos Humanos

We calculate the critical parameters for some simple quantum wells by means of the Riccati?Padé method. The original approach converges reasonably well for nonzero angularmomentum quantum numberlbut rather too slowly for thesstates. We therefore proposea simple modification that yields remarkably accurate results for the latter case. The rate ofconvergence of both methods increases withland decreases with the radial quantum numbern. We compare RPM results with WKB ones for sufficiently large values of l. As illustrative examples we choose the one-dimensional and central-field Gaussian wells as well asthe Yukawa potential. The application of perturbation theory by means of the RPM to aclass of rational potentials yields interesting and baffling unphysical results.