Schrödinger evolution of superoscillations with delta- and delta'-potentials

Jussi Behrndt, Yakir Aharonov, Fabrizio Colombo, Peter Schlosser

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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
Original languageEnglish
Pages (from-to)293-305
JournalQuantum Studies: Mathematics and Foundations
Publication statusPublished - 2020

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