Aharonov–Berry superoscillations in the radial harmonic oscillator potential

D. Alpay; F. Colombo; I. Sabadini; D. C. Struppa

doi:10.1007/s40509-019-00206-5

Aharonov–Berry superoscillations in the radial harmonic oscillator potential

D. Alpay
, F. Colombo
, I. Sabadini
, D. C. Struppa

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper, we study the evolutions of Aharonov–Berry superoscillations under the radial harmonic oscillator potential. For this model, we know the Green function and, taking advantage of it, we use a method recently developed for the step potential to show how superoscillations evolve in time. Also in this case, the time evolution is studied using the notion of super-shift of functions.

Original language	English
Pages (from-to)	269-283
Number of pages	15
Journal	Quantum Studies: Mathematics and Foundations
Volume	7
Issue number	3
DOIs	https://doi.org/10.1007/s40509-019-00206-5
State	Published - 1 Sep 2020
Externally published	Yes

Keywords

Convolution operators
Entire functions with growth conditions
Schrödinger equation
Superoscillating functions

ASJC Scopus subject areas

Atomic and Molecular Physics, and Optics
Mathematical Physics

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10.1007/s40509-019-00206-5

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title = "Aharonov–Berry superoscillations in the radial harmonic oscillator potential",

abstract = "In this paper, we study the evolutions of Aharonov–Berry superoscillations under the radial harmonic oscillator potential. For this model, we know the Green function and, taking advantage of it, we use a method recently developed for the step potential to show how superoscillations evolve in time. Also in this case, the time evolution is studied using the notion of super-shift of functions.",

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AU - Colombo, F.

AU - Sabadini, I.

AU - Struppa, D. C.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - In this paper, we study the evolutions of Aharonov–Berry superoscillations under the radial harmonic oscillator potential. For this model, we know the Green function and, taking advantage of it, we use a method recently developed for the step potential to show how superoscillations evolve in time. Also in this case, the time evolution is studied using the notion of super-shift of functions.

AB - In this paper, we study the evolutions of Aharonov–Berry superoscillations under the radial harmonic oscillator potential. For this model, we know the Green function and, taking advantage of it, we use a method recently developed for the step potential to show how superoscillations evolve in time. Also in this case, the time evolution is studied using the notion of super-shift of functions.

KW - Convolution operators

KW - Entire functions with growth conditions

KW - Schrödinger equation

KW - Superoscillating functions

UR - https://www.scopus.com/pages/publications/85091759056

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DO - 10.1007/s40509-019-00206-5

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ER -

Aharonov–Berry superoscillations in the radial harmonic oscillator potential

Abstract

Keywords

ASJC Scopus subject areas

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