Variational Approximations in a Path-Integral Description of Potential Scattering
arXiv:0912.4429 · doi:10.1140/epja/i2010-10996-8
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.
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
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