Eur. Phys. J. Plus (2016) 131: 306
https://doi.org/10.1140/epjp/i2016-16306-1

Regular Article

Downward relativistic potential step and phenomenological account of Bohmian trajectories of the Klein paradox

¹ Department of Physics, Islamic Azad University, Mashhad Branch, 91735-413, Mashhad, Iran
² Department of Physics, Khayyam Higher Education Institute (KHEI), Mashhad, Iran
³ School of Physics, Institute for Research in Fundamental Science (IPM), Tehran, Iran

^* e-mail: mollai.razavi@gmail.com

Received: 6 April 2016
Revised: 19 July 2016
Accepted: 2 August 2016
Published online: 9 September 2016

Abstract

The Dirac equation has been applied to fermions scattering from the downward potential step. The results show that some particles do not fall off the edge of the step and reflect. Then, based on the de Broglie-Bohm interpretation of quantum mechanics (Bohmian mechanics) and Bohmian trajectories we have resolved the problem. Lastly, a phenomenological study of the Bohmian trajectory of the Klein paradox has been discussed.