Transmission resonances and supercritical states in a one dimensional cusp potential

TL;DR

This paper analyzes the Dirac equation with a symmetric cusp potential, identifying conditions for transmission resonances and supercritical states through exact solutions for scattering and bound states.

Contribution

It provides a novel analytical solution to the Dirac equation with a cusp potential and derives conditions for transmission resonances and supercriticality.

Findings

Derived conditions for transmission resonances.

Identified criteria for supercritical states.

Solved for scattering and bound states explicitly.

Abstract

We solve the two-component Dirac equation in the presence of a spatially one dimensional symmetric cusp potential. We compute the scattering and bound states solutions and we derive the conditions for transmission resonances as well as for supercriticality.