Regular Article

Localization in one-dimensional relativistic quantum mechanics

¹ St. Xavier’s College, Mumbai 400001, India
² Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India
³ Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
⁴ UM-DAE Centre for Excellence in Basic Sciences, University of Mumbai, Vidynagari Campus, Mumbai 400098, India

^a e-mail: sjoshi@barc.gov.in

Received: 20 November 2019
Published online: 3 February 2020

Abstract

We present the relativistic analogue of Anderson localization in one dimension. We use Dirac equation to calculate the transmission probability for a spin-½ particle incident upon a rectangular barrier. Using the transfer matrix formalism, we numerically compute the transmission probability for the case of a large number of identical barriers spread randomly in one dimension. The particular case when the incident particle has three component momentum and shows spin-flip phenomena is also considered. Our calculations suggest that the incident relativistic particle shows localization behaviour similar to that of Anderson localization. A number of results which are generalizations of the non-relativistic case are also obtained.