(1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: Effectively PT-symmetric

Abstract

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1 + 1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the “quasi-parity” on the Dirac particles’ spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z) = S(x − ib) (an inversely linear plus linear, leading to a PT −symmetric oscillator model), and S(x) = Sr(x) + iSi(x) (a PT -symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an η-weak-pseudo-Hermiticity generator are presented and a complexified PT -symmetric periodic-type model is used as an illustrative example.