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\((1+1)\)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: Effectively \(\mathcal{PT}\)-symmetric. (English) Zbl 1140.81363

Summary: 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 \(S (x)= S_{r}(x)+ iS_{i}(x) (a \mathcal{PT}\) -symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an \(\eta\)-weak-pseudo-Hermiticity generator are presented and a complexified \(\mathcal{PT}\) -symmetric periodic-type model is used as an illustrative example.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q60 Supersymmetry and quantum mechanics
78A35 Motion of charged particles
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