Article contents
A characterization of singular Schrödinger operators on the half-line
Published online by Cambridge University Press: 07 December 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 $\mathbb {R}^3$ , 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.
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2020
Footnotes
The research of L.L.B. was supported by grant P 30821-N35 of the Austrian Science Fund FWF, and the research of K.S was supported by grant P 30821-N35 of the Austrian Science Fund FWF.
References
- 2
- Cited by