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Title: On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging
Authors: Athanassoulis, Agisilaos
Antonelli, P.
Markowich, P. A.
Hajaiej, H.
First Published: 14-Jan-2014
Publisher: Springer Berlin Heidelberg
Citation: Archive for Rational Mechanics and Analysis, 2014, 211 (3), pp. 711-732
Abstract: We analyse a nonlinear Schrödinger equation for the time-evolution of the wave function of an electron beam, interacting selfconsistently through a Hartree–Fock nonlinearity and through the repulsive Coulomb interaction of an atomic nucleus. The electrons are supposed to move under the action of a time dependent, rapidly periodically oscillating electromagnetic potential. This can be considered a simplified effective single particle model for an X-ray free electron laser. We prove the existence and uniqueness for the Cauchy problem and the convergence of wave-functions to corresponding solutions of a Schrödinger equation with a time-averaged Coulomb potential in the high frequency limit for the oscillations of the electromagnetic potential.
DOI Link: 10.1007/s00205-013-0715-8
ISSN: 0003-9527
eISSN: 1432-0673
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2014, Springer-Verlag Berlin Heidelberg. All rights reserved. The final publication is available at Springer via
Appears in Collections:Published Articles, Dept. of Mathematics

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