Geodesic
A characterization of singular Schrödinger operators on the half-line
Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 923-941

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DOI

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 $\mathbb {R}^3$, in the case of radial potentials. Moreover, we discuss explicitly our results in the case of potentials that are linear in a neighborhood of the origin.
DOI : 10.4153/S0008439520000958
Mots-clés : Schrödinger operators, singular perturbations, point interactions, nonstandard analysis 
Scandone, Raffaele; Baglini, Lorenzo Luperi; Simonov, Kyrylo. A characterization of singular Schrödinger operators on the half-line. Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 923-941. doi: 10.4153/S0008439520000958
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     author = {Scandone, Raffaele and Baglini, Lorenzo Luperi and Simonov, Kyrylo},
     title = {A characterization of singular {Schr\"odinger} operators on the half-line},
     journal = {Canadian mathematical bulletin},
     pages = {923--941},
     year = {2021},
     volume = {64},
     number = {4},
     doi = {10.4153/S0008439520000958},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000958/}
}
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