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

## TL;DR

This paper investigates the spectral properties of a one-dimensional Dirac Hamiltonian with delta-function impurities, analyzing how different types of potentials affect bound and scattering states of fermions.

## Contribution

It provides a detailed comparison of the spectral effects of mass-spike versus electrostatic delta potentials in 1D Dirac systems, highlighting their differences.

## Key findings

- Spectral differences between mass-spike and electrostatic delta potentials
- Bound and scattering states characterized for each potential type
- Thorough exploration of potential-dependent spectral features

## 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. We distinguish between "mass-spike" and "electrostatic" $\delta$-potentials. Differences in the spectra arising depending on the type of $\delta$-potential studied are thoroughly explored.