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arXiv · 2004.04212

A characterization of singular Schr\"odinger operators on the half-line

Raffaele Scandone·Lorenzo Luperi Baglini·Kyrylo Simonov
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Abstract

We study a class of delta-like perturbations of the Laplacian on the half-line, characterized by Robin boundary conditions at the origin. Using the formalism of nonstandard analysis, we derive a simple connection with a suitable family of Schr\"{o}dinger operators with potentials of very large (infinite) magnitude and very short (infinitesimal) range. As a consequence, we also derive a similar result for point interactions in the Euclidean space $\mathbb{R}^3$, in the case of radial potentials. Moreover, we discuss explicitly our results in the case of potentials that are linear in a neighbourhood of the origin.

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Raffaele Scandone, Lorenzo Luperi Baglini, Kyrylo Simonov. 2020-04-08. A characterization of singular Schr\"odinger operators on the half-line. https://doi.org/10.4153/s0008439520000958

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