Eur. Phys. J. A (2010) 45: 193-215
https://doi.org/10.1140/epja/i2010-10996-8

Regular Article - Theoretical Physics

Variational approximations in a path integral description of potential scattering

Particle Theory Group, Paul Scherrer Institute, CH-5232, Villigen PSI, Switzerland

^* e-mail: roland.rosenfelder@psi.ch

Received: 19 March 2010
Accepted: 27 May 2010
Published online: 2 July 2010

Abstract

Using a recent path integral representation for the T -matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables --over which one has to integrate functionally-- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading). We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fail.