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

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 ent...

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Bibliographic Details
Published in:Quantum Studies : Mathematics and Foundations 2020-09, Vol.7 (3), p.293-305
Main Authors: Aharonov, Yakir, Behrndt, Jussi, Colombo, Fabrizio, Schlosser, Peter
Format: Article
Language:English
Subjects:
Convergence
Convolution
Entire functions
Evolution
Function space
History and Philosophical Foundations of Physics
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Mathematics and Statistics
Operators (mathematics)
Plane waves
Quantum Physics
Regular Paper
Schrodinger equation
Theoretical
Time dependence
Topology
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Summary: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 A 1 ( 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.
ISSN:2196-5609
2196-5617
DOI:10.1007/s40509-019-00215-4