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The scattering wavefunction as a propagator

The relation between the scattering wavefunction Psi (r1) and the propagator K(r1,t1 mod p0,t0) is established for a short-range potential by means of the Moller operator. The semiclassical approximation to the propagator provides the usual asymptotic formula for Psi (r1) where the scattering amplitude is substantiated by its semiclassical expression. An extension of this method to include a Coulomb potential provides similar results. The inelastic scattering case is then considered and the excitation wavefunction Psi beta alpha (r1) is expressed in terms of the reduced propagator Kbeta alpha (r1,t1 mod p0,t0). An expression for the excitation cross section in terms of Kbeta alpha (r1,t1 mod p0, t0) is finally obtained.