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.

13 pages, 1 figure