Approximation of Schrödinger operators with point interactions on bounded domains
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918047189565440 |
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| author | Noja, Diego Scandone, Raffaele |
| author_facet | Noja, Diego Scandone, Raffaele |
| contents | We consider Schrödinger operators on a bounded domain $Ω\subset \mathbb{R}^3$, with homogeneous Robin or Dirichlet boundary conditions on $\partialΩ$ and a point (zero-range) interaction placed at an interior point of $Ω$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation of Schrödinger operators with point interactions on bounded domains Noja, Diego Scandone, Raffaele Mathematical Physics We consider Schrödinger operators on a bounded domain $Ω\subset \mathbb{R}^3$, with homogeneous Robin or Dirichlet boundary conditions on $\partialΩ$ and a point (zero-range) interaction placed at an interior point of $Ω$. 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. |
| title | Approximation of Schrödinger operators with point interactions on bounded domains |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2412.16056 |