Document Type
Article
Publication Date
12-13-2019
Abstract
In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schrödinger equation with δ- and δ′-potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converge in the topology of the entire function space A1(C). Convolution operators acting in this space are our main tool. In particular, a general result about the existence of such operators is proven. Moreover, we provide an explicit formula as well as the large time asymptotics for the time evolution of a plane wave under δ- and δ′-potentials.
Recommended Citation
Aharonov, Y., Behrndt, J., Colombo, F. et al. Schrödinger evolution of superoscillations with δ- and δ′-potentials. Quantum Stud.: Math. Found. 7, 293–305 (2020). https://doi.org/10.1007/s40509-019-00215-4
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 Quantum Studies: Mathematics and Foundations, volume 7, in 2020. https://doi.org/10.1007/s40509-019-00215-4