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The European Physical Journal A

, Volume 45, Issue 2, pp 193–215 | Cite as

Variational approximations in a path integral description of potential scattering

  • J. Carron
  • R. RosenfelderEmail author
Regular Article - Theoretical Physics

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.

Keywords

Variational Principle Variational Equation Eikonal Approximation Potential Scattering Reference Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Particle Theory GroupPaul Scherrer InstituteVilligen PSISwitzerland

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