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|Title:||On the XFEL Schrödinger Equation: Highly Oscillatory Magnetic Potentials and Time Averaging|
Markowich, P. A.
|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.|
|Rights:||Copyright © 2014, Springer-Verlag Berlin Heidelberg. All rights reserved. The final publication is available at Springer via http://dx.doi.org/10.1007/s00205-013-0715-8|
|Appears in Collections:||Published Articles, Dept. of Mathematics|
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|Antonelli et al. - 2014 - On the XFEL Schrodinger Equation Highly Oscillatory Magnetic Potentials and Time Averaging.pdf||Post-review (final submitted)||342.2 kB||Adobe PDF||View/Open|
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