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.
| Original language | English |
|---|---|
| Pages (from-to) | 711-732 |
| Number of pages | 22 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 211 |
| Issue number | 3 |
| Early online date | 14 Jan 2014 |
| DOIs | |
| Publication status | Published - Mar 2014 |
Keywords
- Weak Convergence
- Admissible Pair
- Uniform Bound
- Strichartz Estimate
- Electromagnetic Potential
ASJC Scopus subject areas
- Analysis
- Mechanical Engineering
- Mathematics (miscellaneous)
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