General properties of potentials admitting the solution of the Schroedinger equation by means of the hypergeometric functions

Problem of constructing the Jost function and the S-matrix for a family of potential curves admitting the solution of the s-wave Schroedinger equation by means of the hyper-geometric series is considered in a general form. Asymptotically Coulomb potentials are determined in the limit of the confluent hypergeometric equation. For the case mentioned, the Green function is represented as the product of two Whittaker functions. Thus various partial results obtained by a number of authors for potentials given explicity are summarized