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arXiv · 1305.3805

On contact interactions as limits of short-range potentials

Gerhard Bräunlich·Christian Hainzl·Robert Seiringer
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Abstract

We reconsider the norm resolvent limit of $-Δ+ V_\ell$ 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.

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Gerhard Bräunlich, Christian Hainzl, Robert Seiringer. 2013-05-16. On contact interactions as limits of short-range potentials. https://arxiv.org/abs/1305.3805

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