Variational Approximations in a Path-Integral Description of Potential Scattering
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.
Cite
@article{arxiv.0912.4429,
title = {Variational Approximations in a Path-Integral Description of Potential Scattering},
author = {J. Carron and R. Rosenfelder},
journal= {arXiv preprint arXiv:0912.4429},
year = {2010}
}
Comments
35 pages, 3 figures, 6 tables, Latex with amsmath, amssymb; v2: 28 pages, EPJ style, misprints corrected, note added about correct treatment of complex Gaussian integrals with the theory of "pencils", matches published version