Scattering of a Dirac electron on a mass barrier

TL;DR

This paper studies how a Dirac electron wave packet interacts with a mass barrier in one dimension, revealing features like wave packet compression, penetration, and wave tails, using Fourier integral methods.

Contribution

It introduces a detailed analysis of wave packet scattering on a mass barrier, highlighting features specific to two-dimensional wave packets and employing Fourier integral techniques.

Findings

Wave packet compression during reflection

Penetration below barrier energy levels

Wave tails and precursors observed

Abstract

The interaction of a wave packet (and in particular the wave front) with a mass barrier is investigated in one dimension. We discuss the main features of the wave packet that are inherent to two-dimensional wave packets, such as compression during reflection, penetration in the case when the energy is lower than the height of the barrier, waving tails, precursors, and the retardation of the reflected and penetrated wave packets. These features depend on the wave-packet envelope function which we demonstrate by considering the case of a rectangular wave packet with sharp front and trailing edges and a smooth Gaussian wave packet. The method of Fourier integral for obtaining the nonstationary solutions is used.