Document Type
Article
Publication Date
1-8-2021
Abstract
In this paper we study the time dependent Schrödinger equation with all possible self-adjoint singular interactions located at the origin, which include the δ and δ'-potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study the stability and oscillatory properties of the solution of the Schrödinger equation subject to a generalized point interaction when the initial datum is a superoscillatory function.
Recommended Citation
Y. Aharonov, J. Behrndt, F. Colombo, P. Schlosser, Green’s function for the Schrödinger equation with a generalized point interaction and stability of superoscillations. Journal of Differential Equations 277 (2021) 153–190. https://doi.org/10.1016/j.jde.2020.12.029
Peer Reviewed
1
Copyright
The authors
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Comments
This article was originally published in Journal of Differential Equations, volume 277, in 2021. https://doi.org/10.1016/j.jde.2020.12.029