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arXiv · 0912.4429

Variational Approximations in a Path-Integral Description of Potential Scattering

J. Carron·R. Rosenfelder
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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.

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J. Carron, R. Rosenfelder. 2010-08-24. Variational Approximations in a Path-Integral Description of Potential Scattering. https://doi.org/10.1140/epja%2Fi2010-10996-8

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