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 Schrödinger 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 R3, 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.
A characterization of singular Schrödinger operators on the half-line / R. Scandone, L. Luperi Baglini, K. Simonov. - In: CANADIAN MATHEMATICAL BULLETIN. - ISSN 1496-4287. - (2020). [Epub ahead of print] [10.4153/S0008439520000958]
A characterization of singular Schrödinger operators on the half-line
L. Luperi Baglini;
2020
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 Schrödinger 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 R3, 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.File | Dimensione | Formato | |
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