Closed-form solutions of the Schroedinger equation for a class of smoothed Coulomb potentials

Abstract

An infinite family of closed-form solutions is exhibited for the Schroedinger equation for the potential $V(r) = -Z/\sqrt{|r|^{2} + a^{2}}$. Evidence is presented for an approximate dynamical symmetry for large values of the angular momentum $l$.Comment: 13 pages LaTeX, uses included Institute of Physics style files, 3 PostScript figures. In press at J. Phys. B: At. Mol. Opt. Phys. (1997