AUTHOR=Guilarte Juan Mateos , Munoz-Castaneda Jose M. , Pirozhenko Irina , Santamaría-Sanz Lucia 

TITLE=One-Dimensional Scattering of Fermions on δ-Impurities

JOURNAL=Frontiers in Physics

VOLUME=Volume 7 - 2019

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00109

DOI=10.3389/fphy.2019.00109

ISSN=2296-424X

ABSTRACT=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.