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    On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging

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    Type
    Article
    Authors
    Antonelli, Paolo
    Athanassoulis, Agisillaos
    Hajaiej, Hichem
    Markowich, Peter A. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Date
    2014-01-14
    Preprint Posting Date
    2012-09-26
    Online Publication Date
    2014-01-14
    Print Publication Date
    2014-03
    Permanent link to this record
    http://hdl.handle.net/10754/563339
    
    Metadata
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    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. © 2014 Springer-Verlag Berlin Heidelberg.
    Citation
    Antonelli, P., Athanassoulis, A., Hajaiej, H., & Markowich, P. (2014). On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging. Archive for Rational Mechanics and Analysis, 211(3), 711–732. doi:10.1007/s00205-013-0715-8
    Sponsors
    P. Antonelli and A. Athanassoulis would like to thank the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge for its hospitality and support during the preparation of this work. This research was supported by the Investigator Award Nr. KUK-I1-007-43 funded by the King Abdullah University of Science and Technology. H. Hajaiej extends his appreciation to the deanship of scientific research at King Saud University through the research group project RGP-VPP124.
    Publisher
    Springer Nature
    Journal
    Archive for Rational Mechanics and Analysis
    DOI
    10.1007/s00205-013-0715-8
    arXiv
    1209.6089
    Additional Links
    http://arxiv.org/abs/arXiv:1209.6089v1
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00205-013-0715-8
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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