(1+1)-Dirac bound states in one dimension, with position-dependent Fermi velocity and mass

Abstract

We extend Panella and Roy's [17] work for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where the mass and velocity are both position-dependent. Bound states in the continuum (BIC)-like and discrete bound state solutions are reported. It is observed that BIC-like solutions are not only feasible for the ultra-relativistic (massless) Dirac particles but also for Dirac particles with PDmass and PD-velocity that satisfy the condition m(x) v (F) (2) (x) = A, where A a parts per thousand yen 0 is constant. Dirac Poschl-Teller and harmonic oscillator models are also reported.