Scattering states of Dirac particle equation with position dependent mass under the cusp potential

TL;DR

This paper solves the one-dimensional Dirac equation with position-dependent mass under a cusp potential, deriving reflection and transmission coefficients and analyzing how mass variation affects these coefficients.

Contribution

It provides exact solutions using Whittaker functions for the Dirac equation with position-dependent mass in a cusp potential, including new insights into scattering properties.

Findings

Mass variation significantly influences reflection and transmission coefficients.

Explicit expressions for wave functions in terms of Whittaker functions.

Analysis of how the cusp potential affects particle scattering.

Abstract

We solved the one-dimensional position-dependent mass Dirac equation in the presence of the cusp potential and reported the solutions in terms of the Whittaker functions. We have derived the reflection and transmission coefficients by making use of the matching conditions on the wave functions. The effect of position dependent mass on the reflection and transmission coefficients of the system is duly investigated.