The classical trajectory in nonrelativistic scattering
Abstract
Being guided by the Statistical interpretation of quantum mechanics, 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 projectilenucleus 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 which is inherent in the Glauber theory.
 Publication:

Ph.D. Thesis
 Pub Date:
 May 1978
 Bibcode:
 1978PhDT........35W
 Keywords:

 Nonrelativistic Mechanics;
 Particle Trajectories;
 Quantum Mechanics;
 Approximation;
 Feynman Diagrams;
 Glauber Theory;
 Scattering Functions;
 Wave Functions;
 Thermodynamics and Statistical Physics