Exact Solutions of Effective Mass Dirac Equation with non-PT-Symmetric and non-Hermitian Exponential-type Potentials

TL;DR

This paper derives exact analytical solutions for the one-dimensional effective mass Dirac equation with non-PT-symmetric, non-Hermitian exponential potentials, revealing how such potentials influence bound state energies and wave functions.

Contribution

It introduces a two-component approach to solve the effective mass Dirac equation with new non-PT-symmetric, non-Hermitian potentials, providing explicit energy spectra and eigenfunctions.

Findings

Analytical energy levels obtained for the potentials.

Bound state wave functions explicitly derived.

Mapping of Dirac to Schrödinger-like equation demonstrated.

Abstract

By using two-component approach to the one-dimensional effective mass Dirac equation bound states are investigated under the effect of two new non-PT-symmetric, and non-Hermitian, exponential type potentials. It is observed that the Dirac equation can be mapped into a Schr\"{o}dinger-like equation by rescaling one of the two Dirac wave functions in the case of the position dependent mass. The energy levels, and the corresponding Dirac eigenfunctions are found analytically.