Klein's Paradox and the Relativistic $\delta$-shell Interaction in ${\mathbb{R}}^3$

Albert Mas, Fabio Pizzichillo

Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in ${\mathbb{R}}^3$ coupled with a suitable re-scaling of $\mathbf{V}$ c…