On contact interactions as limits of short-range potentials
The physical applications of Hamiltonians of point interactions defined as extensions of operators require a correct choice of the extension. In particular, in models of cold atomic gases the choice is based on approximation by short-range potentials \(V_l\) with the range \(l\) converging to zero, as \(l\to 0\), while the scattering length tends to a finite limit. The paper provides a rigorous implementation of the above idea. The interaction \(V_l\) is required to have a strong repusive core. An important ingredient is a formula for the scattering length obtained by \textit{C. Hainzl} and \textit{R. Seiringer} [Lett. Math. Phys. 84, No. 2-3, 99--107 (2008; Zbl 1164.81006)].
scientific article; zbMATH DE number 6333564