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Abstract

The radial SCHRÖDINGER equation is considered in a more general form and is then transformed into another equation to permit straightforward application of the perturbation formalism used previously by the author. The potential considered is assumed to be expandable in ascending even powers of r. The potential (sinh r)−2 emerges as a special case and is considered separately. For the general case, expansions are obtained for the eigenenergies and eigenfunctions valid in regions of small angular momenta and coupling constants. A simple analytic expression for the S-matrix is obtained. Finally several consequences are discussed.