Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0912.4429 · The European Physical Journal A

Variational approximations in a path integral description of potential scattering

Julien Carron, R. Rosenfelder

Published Jul 1, 2010• 6 citations
arXivHTMLPDF
DOI
10.1140/epja/i2010-10996-8

Related papers

Path integral representation for inelastic scattering amplitude and its quasiclassical approximations

А. В. Богданов, G. V. Dubrovskiǐ

Theoretical and Mathematical Physics•Feb 1, 1977•4 citations

Two-Dimensional Potential Scattering using the Path Integral Technique

Allison L. Harris, Torrey Saxton, Zachary Temple

Bulletin of the American Physical Society•Nov 7, 2017•0 citations

A new path-integral representation of the T-matrix in potential scattering

Julien Carron, R. Rosenfelder

arXiv:1107.3034•Physics Letters A•Sep 11, 2011•10 citations

The Feynman path integral in potential scattering

Sergio A Albeverio, Raphael J. Høegh-Krohn

Lecture notes in mathematics•Jan 1, 1976•0 citations

Variational Approximations in a Path-Integral Description of Potential Scattering

Julien Carron, R. Rosenfelderb

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

•Aug 14, 2016•8 citations

Variational Methods for Path Integral Scattering

Julien Carron

In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the Feynman-Jensen variational method. A simple Ansatz for the trial action is made, and, in both cases, the variational procedure singles out a particular one-particle classical equation of motion, given in integral form. While the first is real, in the second representation this trajectory is complex and evolves according to an effective, time dependent potential. Using a cumulant expansion, the first correction to the variational approximation is also evaluated. The high energy behavior of the approximation is investigated, and is shown to contain exactly the leading and next-to-leading order of the eikonal expansion, and parts of higher terms. Our results are then numerically tested in two particular situations where others approximations turned out to be unsatisfactory. Substantial improvements are found.

arXiv:0903.0273•Mar 2, 2009•5 citations
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
In this master thesis, a new approximation scheme to non-relativistic potential scattering is developed and discussed. The starting points are two exact path integral representations of the T-matrix, which permit the application of the Feynman-Jensen variational method. A simple Ansatz for the trial action is made, and, in both cases, the variational procedure singles out a particular one-particle classical equation of motion, given in integral form. While the first is real, in the second representation this trajectory is complex and evolves according to an effective, time dependent potential. Using a cumulant expansion, the first correction to the variational approximation is also evaluated. The high energy behavior of the approximation is investigated, and is shown to contain exactly the leading and next-to-leading order of the eikonal expansion, and parts of higher terms. Our results are then numerically tested in two particular situations where others approximations turned out to be unsatisfactory. Substantial improvements are found.