An alternative classical representation of the phase shifts and the inverse scattering problem

A semiclassical expression for the phase shift is derived which contains an integration over the time instead of the distance, as in the standard semiclassical formalism. The implications of this formula are discussed and a theorem is proved which simplifies its manipulation. The perturbative series of the phase shift, up to first order in a small part of the potential, is obtained. It is shown that this new representation of the phase shift provides a solution of the inverse scattering problem. ((orig.))