Schrödinger evolution of superoscillations with δ - and δ -potentials

Yakir Aharonov, Jussi Behrndt*, Fabrizio Colombo, Peter Schlosser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

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.

Original languageEnglish
Pages (from-to)293-305
Number of pages13
JournalQuantum Studies: Mathematics and Foundations
Volume7
Issue number3
DOIs
StatePublished - 1 Sep 2020
Externally publishedYes

Funding

FundersFunder number
TU Graz, Internationale Beziehungen und Mobilitätsprogramme

    Keywords

    • Convolution operators
    • Entire functions with growth conditions
    • Schrödinger equation
    • Singular potential
    • Superoscillating functions

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