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Schrödinger evolution of superoscillations with $δ$- and $δ'$-potentials (1911.04693v1)
Published 12 Nov 2019 in math-ph, math.AP, math.FA, math.MP, and math.SP
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.