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Original Research ARTICLE Provisionally accepted The full-text will be published soon. Notify me

Front. Phys. | doi: 10.3389/fphy.2019.00109

One-dimensional scattering of fermions on $\delta$-impurities

 Juan M. Guilarte1, 2*,  Jose M Munoz-Castaneda3, 4, Lucia Santamaría-Sanz5 and  Irina Pirozhenko6, 7
  • 1University of Salamanca, Spain
  • 2Departamento de Física Fundamental and IUFFyM, Spain
  • 3Departamento de Física Teórica, Atómica y Óptica, Spain
  • 4Universidad de Valladolid, Spain
  • 5Departamento de Física Teórica Atómica y Óptica, Universidad de Valladolid, Spain
  • 6Bogoliubov Laboratory of Theoretical Physics, JINR, Russia
  • 7Dubna State Universit, Russia

We study the spectrum of the 1D Dirac Hamiltonian encompassing the bound and scattering states of a fermion distorted by a static background built from $\delta$-function potentials. After introducing the most general Dirac-$\delta$ potential for the Dirac equation we distinguish between \lq\lq mass-spike\rq\rq and \lq\lq electrostatic\rq\rq $\delta$-potentials. Differences in the spectra arising depending on the type of $\delta$-potential are studied in deep detail.

Keywords: Contact intentions, Diract equation, Dirac delta, Selfadjoint extensions, Relativistic quantum mechanics

Received: 22 Mar 2019; Accepted: 11 Jul 2019.

Edited by:

Luiz A. Manzoni, Concordia College, United States

Reviewed by:

Özlem Yeşiltaş, Gazi University, Turkey
Edilberto O. Silva, Federal University of Maranhão, Brazil  

Copyright: © 2019 Guilarte, Munoz-Castaneda, Santamaría-Sanz and Pirozhenko. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Juan M. Guilarte, University of Salamanca, Salamanca, Spain,