Classical trajectory in non-relativistic scattering

With the statistical interpretation of quantum mechanics as a guide, the classical trajectory is incorporated into quantum scattering theory. The Feynman path integral formalism is used as a starting point, and classical transformation theory is applied to the phase of the wave function so derived. This approach is then used to derive an expression for the scattering amplitude for potential scattering. It is found that the amplitude can be expressed in an impact parameter representation similar to the Glauber formalism. Connections are then made to the Glauber approximation and to semiclassical approximations derived from the Feynman path integral formalism. In extending this analysis to projectile-nucleus scattering, an approximation scheme is given with the first term being the same as in Glauber's multiple scattering theory. Higher-order approximations, thus, are found to give corrections to the fixed scatterer form of the impulse approximation inherent in the Glauber theory