2006/11/30 by Omar Mustafa, S. Habib Mazharimousavi · 1 citation
Mathematics · Physics and Astronomy · #Dirac equation #Geometry #Lorentz transformation #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Parity (physics) #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Scalar (mathematics) #quant-ph
paper · pdf · doi:10.1007/s10773-007-9539-3
published as Int. J. Theor. Phys. 47, 1112 (2008) · 11 pages, no figures, revised
arxiv created 2007/04/12 · openalex publication_date 2007/09/25 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.