A unified approach to Schrödinger evolution of superoscillations and supershifts

Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persisten...

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Autores principales: Aharonov, Yakir, Behrndt, Jussi, Colombo, Fabrizio, Schlosser, Peter
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8918494/
https://www.ncbi.nlm.nih.gov/pubmed/35310834
http://dx.doi.org/10.1007/s00028-022-00770-1
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author Aharonov, Yakir
Behrndt, Jussi
Colombo, Fabrizio
Schlosser, Peter
author_facet Aharonov, Yakir
Behrndt, Jussi
Colombo, Fabrizio
Schlosser, Peter
author_sort Aharonov, Yakir
collection PubMed
description Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper, we give a unified approach to determine the supershift property for the solution of the time-dependent one-dimensional Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green’s function, but not its explicit form. With this efficient general technique, we are able to treat various potentials.
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spelling pubmed-89184942022-03-17 A unified approach to Schrödinger evolution of superoscillations and supershifts Aharonov, Yakir Behrndt, Jussi Colombo, Fabrizio Schlosser, Peter J Evol Equ Article Superoscillating functions and supershifts appear naturally in weak measurements in physics. Their evolution as initial conditions in the time-dependent Schrödinger equation is an important and challenging problem in quantum mechanics and mathematical analysis. The concept that encodes the persistence of superoscillations during the evolution is the (more general) supershift property of the solution. In this paper, we give a unified approach to determine the supershift property for the solution of the time-dependent one-dimensional Schrödinger equation. The main advantage and novelty of our results is that they only require suitable estimates and regularity assumptions on the Green’s function, but not its explicit form. With this efficient general technique, we are able to treat various potentials. Springer International Publishing 2022-03-14 2022 /pmc/articles/PMC8918494/ /pubmed/35310834 http://dx.doi.org/10.1007/s00028-022-00770-1 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Aharonov, Yakir
Behrndt, Jussi
Colombo, Fabrizio
Schlosser, Peter
A unified approach to Schrödinger evolution of superoscillations and supershifts
title A unified approach to Schrödinger evolution of superoscillations and supershifts
title_full A unified approach to Schrödinger evolution of superoscillations and supershifts
title_fullStr A unified approach to Schrödinger evolution of superoscillations and supershifts
title_full_unstemmed A unified approach to Schrödinger evolution of superoscillations and supershifts
title_short A unified approach to Schrödinger evolution of superoscillations and supershifts
title_sort unified approach to schrödinger evolution of superoscillations and supershifts
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8918494/
https://www.ncbi.nlm.nih.gov/pubmed/35310834
http://dx.doi.org/10.1007/s00028-022-00770-1
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