A Schr\"{o}dinger equation for relativistic laser-matter interactions
Abstract
A semi-relativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that relativistic effects induced by a super-intense laser field can, to a surprisingly large extent, be accounted for by the Schr{\"o}dinger equation, provided that we replace the rest mass in the propagation gauge Hamiltonian by the corresponding time-dependent field-dressed mass. The validity of the semi-relativistic approach is tested numerically on a hydrogen atom exposed to an intense XUV laser pulse strong enough to accelerate the electron towards relativistic velocities. It is found that while the results obtained from the ordinary (non-relativistic) Schr{\"o}dinger equation generally differ from those of the Dirac equation, merely demonstrating that relativistic effects are significant, the semi-relativistic formulation provides results in quantitative agreement with a fully relativistic treatment.
Cite
@article{arxiv.1809.05295,
title = {A Schr\"{o}dinger equation for relativistic laser-matter interactions},
author = {Tor Kjellsson Lindblom and Morten Førre and Eva Lindroth and Sølve Selstø},
journal= {arXiv preprint arXiv:1809.05295},
year = {2018}
}