Above Barrier Dirac Multiple Scattering and Resonances

TL;DR

This paper extends above barrier analysis from the Schrödinger to the Dirac equation, demonstrating multiple scattering, interference effects, and resonances with numerical illustrations.

Contribution

It introduces a Dirac equation-based analysis of above barrier scattering, revealing infinite reflected and transmitted wave packets and resonance phenomena.

Findings

Perfect agreement with Schrödinger results

Existence of multiple reflected and transmitted wave packets

Resonance phenomena under total overlap conditions

Abstract

We extend an above barrier analysis made with the Schrodinger equation to the Dirac equation. We demonstrate the perfect agreement between the barrier results and back to back steps. This implies the existence of multiple (indeed infinite) reflected and transmitted wave packets. These packets may be well separated in space or partially overlap. In the latter case interference effects can occur. For the extreme case of total overlap we encounter resonances. The conditions under which resonance phenomena can be observed is discussed and illustrated by numerical calculations.