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Approximation of Schrödinger operators with point interactions on bounded domains
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Approximation of Schrödinger operators with point interactions on bounded domains
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Paper
Approximation of Schrödinger operators with point interactions on bounded domains
2024
Overview
We consider Schr\"odinger operators on a bounded domain \\(\\Omega\\subset \\mathbb{R}^3\\), with homogeneous Robin or Dirichlet boundary conditions on \\(\\partial\\Omega\\) and a point (zero-range) interaction placed at an interior point of \\(\\Omega\\). We show that, under suitable spectral assumptions, and by means of an extension-restriction procedure which exploit the already known result on the entire space, the singular interaction is approximated by rescaled sequences of regular potentials. The result is missing in the literature, and we also take the opportunity to point out some general issues in the approximation of point interactions and the role of zero energy resonances.
Publisher
Cornell University Library, arXiv.org
