The Dirac impenetrable barrier in the limit point of the Klein energy zone

Abstract We reanalyze the problem of a 1D Dirac single particle colliding with electrostatic potential step height V 0 positive incoming energy that tends to limit point so-called Klein zone, i.e. E → − m c 2 , for given . In such case, is actually an impenetrable barrier. fact, + relativistic ( < ), maximum value can reach and ensures perfect impenetrability Nevertheless, we note that, unlike nonrelativistic entire eigensolution does not completely vanish, either at barrier or in region under step, but its upper component satisfy Dirichlet boundary condition More importantly, by calculating mean force exerted wall on this eigenstate taking limit, recover required result. use two different approaches obtain latter results. one these approaches, corresponding type quantum force. Throughout article, various issues related transmitted solutions problem, barriers conditions are also discussed. particular, if negative-energy solution used, lower scattering satisfies barrier, external when seem be compatible existence