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arXiv · 1911.04693

Schr\"odinger evolution of superoscillations with $\delta$- and $\delta'$-potentials

Yakir Aharonov·Jussi Behrndt·Fabrizio Colombo·Peter Schlosser
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Abstract

In this paper we study the time persistence of superoscillations as the initial data of the time dependent Schr\"odinger equation with $\delta$- and $\delta'$-potentials. It is shown that the sequence of solutions converges uniformly on compact sets, whenever the initial data converges in the topology of the entire function space $A_1(\mathbb{C})$. 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 $\delta$- and $\delta'$-potentials.

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Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser. 2019-11-12. Schr\"odinger evolution of superoscillations with $\delta$- and $\delta'$-potentials. https://arxiv.org/abs/1911.04693

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