Abstract
The validity of a well known on-shell representation of the perturbed Green operator is extended to cover the fully off-shell case. Based on this result, an integral representation of the off-the-energy-shell transition matrix is derived. The dynamical input to the formulae consists solely of a pair of solutions of the Schrodinger equation taken at the resolvent energy. As an example, the off-shell t matrix is calculated for S-wave scattering by a square well.