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.
