(1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively $\mathcal{PT}$ -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 \(\mathcal{PT-}\) symmetric oscillator model), and S(x)=Sr(x)+iSi(x) (a \(\mathcal{PT}\) -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 \(\mathcal{PT}\) -symmetric periodic-type model is used as an illustrative example.