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arXiv:1305.3805

On contact interactions as limits of short-range potentials

Gerhard Bräunlich, Christian Hainzl, Robert Seiringer

Published May 16, 2013• 3 citations
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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.

DOI
10.48550/arxiv.1305.3805

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Quantum systems composed of NNN distinct particles in R2\R^2R2 with two-body contact interactions of TMS type are shown to arise as limits - in the norm resolvent sense - of Schrodinger operators with suitably rescaled potentials.
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