One-Dimensional Scattering of Fermions on δ-Impurities - Guilarte, Juan Mateos; Munoz-Castaneda, Jose M.; Pirozhenko, Irina; Santamaría-Sanz, Lucia (Frontiers in Physics, 2019)
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 δ-function potentials. After introducing the most general Dirac-δ potential for the Dirac equation we distinguish between “mass-spike” and “electrostatic” δ-potentials. Differences in the spectra arising depending on the type of δ-potential are studied in deep detail.