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

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.

arXiv comment18 pages and 4 figures. Submitted for publication; We have corrected some typos added one new figure and changed the plots for the charge density, as well as added 5 extra references

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Cited by in corpus (8)

• Band spectra of periodic hybrid $\delta$-${\delta }^{\prime }$ structures
• Bound states of a one-dimensional Dirac equation with multiple delta-potentials
• One-dimensional scattering of fermions in double Dirac delta potentials
• Casimir energy for spinor fields with $\delta$-shell potentials
• Effective quantum electrodynamics: One-dimensional model of the relativistic hydrogen-like atom
• On 3D and 1D Weyl particles in a 1D box
• Zero-range potentials for Dirac particles: Bound-state problems
• Bound States and Resonance Analysis of One-Dimensional Relativistic Parity-Symmetric Two Point Interactions