Document Type


Publication Date



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.


This article was originally published in Quantum Studies: Mathematics and Foundations, volume 7, in 2020.

Peer Reviewed



The authors

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.