1 results
A characterization of singular Schrödinger operators on the half-line
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 64 / Issue 4 / December 2021
- Published online by Cambridge University Press:
- 07 December 2020, pp. 923-941
- Print publication:
- December 2021
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- Article
- Export citation
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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.
