Dirac equation with Morse potetnial under the influence of position-dependent mass and local Fermi velocity

TL;DR

This paper solves the one-dimensional Dirac equation with a Morse potential considering position-dependent mass and local Fermi velocity, providing closed-form solutions for wave functions and energy levels.

Contribution

It introduces a novel approach by incorporating position-dependent mass and local Fermi velocity into the Dirac equation with Morse potential, deriving analytical solutions.

Findings

Closed-form wave functions obtained

Energy levels explicitly calculated

Extended scheme enhances understanding of Dirac systems

Abstract

We solve the one-dimensional Dirac equation by taking into account the possibility of position-dependence in the mass function. We also take the Fermi velocity to act as a local variable and examine the combined effects of the two on the solvability of the Dirac equation with respect to the Morse potential. Our results for the wave functions and the energy levels corresponding to such an extended scheme are furnished in closed forms.