Approximation methods in the theory of scattering

The quantum theory of scattering is discussed from the point of view of a time independent formulation. A detailed discussion of the replacement of the ordinary integral equation of scattering by two others is given together with a discussion of the desirability of this procedure both from a physical and mathematical point of view. Variational formulations of these equations are given and their accuracy is indicated by comparison with examples for which exact solutions are known. An exactly soluble problem given by Blatt is treated from the standpoint of the present paper. A formal solution of the general scattering problem is developed and illustrated with Blatt's example.