Transmission resonances for a Dirac particle in a one-dimensional Hulth\'en potential

TL;DR

This paper provides an exact solution to the Dirac equation with a one-dimensional Hulthén potential, analyzing scattering states, reflection and transmission coefficients, and the conditions for transmission resonances based on potential shape.

Contribution

It presents an exact analytical solution for the Dirac equation with Hulthén potential and explores how transmission resonances depend on potential shape.

Findings

Exact solutions for Dirac scattering states in Hulthén potential

Derived conditions for transmission resonances

Showed the influence of potential shape on resonance conditions

Abstract

We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulth\'en potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have calculated the reflection and transmission coefficients by the matching conditions on the wavefunctions, and investigated the condition for the existence of transmission resonances. Furthermore, we have demonstrated how the transmission-resonance condition depends on the shape of the potential.