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

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 η-pseudo-hermetic(η-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 Pöschl-teller complex and Eckart potentials will be discussed as examples.