A Schr\"{o}dinger equation for relativistic laser-matter interactions

TL;DR

This paper introduces a semi-relativistic Schrödinger equation formulation for laser-matter interactions that accurately captures relativistic effects by incorporating a field-dressed mass, validated through numerical simulations on hydrogen atoms under intense laser pulses.

Contribution

The paper develops a semi-relativistic Schrödinger equation using the propagation gauge and relativistic mass shift, providing a computationally simpler yet accurate alternative to fully relativistic models.

Findings

Semi-relativistic Schrödinger equation matches fully relativistic results.

Relativistic effects can be effectively modeled by a mass shift in the Schrödinger equation.

Non-relativistic Schrödinger results significantly differ from relativistic ones.

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.