Schrödinger evolution of superoscillations with δ - and δ′ -potentials

Yakir Aharonov; Jussi Behrndt; Fabrizio Colombo; Peter Schlosser

doi:10.1007/s40509-019-00215-4

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 journal › Article › peer-review

19 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 language	English
Pages (from-to)	293-305
Number of pages	13
Journal	Quantum Studies: Mathematics and Foundations
Volume	7
Issue number	3
DOIs	https://doi.org/10.1007/s40509-019-00215-4
State	Published - 1 Sep 2020
Externally published	Yes

Funding

Funders	Funder number
TU Graz, Internationale Beziehungen und Mobilitätsprogramme

Keywords

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

Access to Document

10.1007/s40509-019-00215-4

Cite this

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abstract = "In this paper, we study the time persistence of superoscillations as the initial data of the time-dependent Schr{\"o}dinger 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.",

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