On contact interactions as limits of short-range potentials

Abstract

We reconsider the norm resolvent limit of $-\Delta + V_\ell$ with $V_\ell$ tending to a point interaction in three dimensions. We are mainly interested in potentials $V_\ell$ modelling short range interactions of cold atomic gases. In order to ensure stability the interaction $V_\ell$ is required to have a strong repulsive core, such that $\lim_{\ell \to 0} \int V_\ell >0$. This situation is not covered in the previous literature.