Position dependent effective mass and pseudo-hermetic generator in Hamiltonians with PT symmetry

TL;DR

This paper introduces a method for solving PT-symmetric non-Hermitian potentials with position-dependent effective mass, applying it to Dirac equations and specific complex potentials, revealing real energy spectra.

Contribution

It develops a general approach to handle PT-symmetric non-Hermitian Hamiltonians with position-dependent mass, including new solutions for Dirac equations and complex potentials.

Findings

Real energy spectra obtained for PT-symmetric potentials

Method applicable to Dirac equations with position-dependent mass

Examples include P"oschl-Teller and Eckart potentials

Abstract

In this paper we present a general method to solve non hermetic potentials with PT symmetry using the introduction of two first-order operator against {\eta}-pseudo-hermetic({\eta}-weak-pseudo-hermiticity) with position dependent effective mass and applying it to Dirac equation with spinor wave function and non-hermitic potentials with real energy spectrum considering position dependent effective mass. Also P\"oschl-teller complex and Eckart potentials will be discussed as examples.