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Few generalized entropic relations related to Rydberg atoms
We calculate the analytical and numerical values of the position space Shannon entropy, momentum space Shannon entropy, and total Shannon entropy, [Formula: see text] , [Formula: see text] , and [Formula: see text] , respectively, of free and trapped Rydberg hydrogen-like atoms. The influence of ato...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9076694/ https://www.ncbi.nlm.nih.gov/pubmed/35523799 http://dx.doi.org/10.1038/s41598-022-10854-0 |
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author | Kumar, Kirtee Prasad, Vinod |
author_facet | Kumar, Kirtee Prasad, Vinod |
author_sort | Kumar, Kirtee |
collection | PubMed |
description | We calculate the analytical and numerical values of the position space Shannon entropy, momentum space Shannon entropy, and total Shannon entropy, [Formula: see text] , [Formula: see text] , and [Formula: see text] , respectively, of free and trapped Rydberg hydrogen-like atoms. The influence of atomic number Z, the principal quantum number n, and energy E on the Shannon entropy of the Rydberg atoms are illustrated. The scaling properties of Shannon entropy with energy of states E and the principal quantum number n have been reported for the first time to the best of our knowledge. Our work explains how Shannon entropy indicates localization-delocalization of the wavefunction. The total Shannon entropy as a measure of the number of nodes in the trapped Rydberg atom’s wavefunction is also discussed. We show why an uncertainty relation based on Shannon entropy is superior to Heisenberg uncertainty for Rydberg atoms. |
format | Online Article Text |
id | pubmed-9076694 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-90766942022-05-08 Few generalized entropic relations related to Rydberg atoms Kumar, Kirtee Prasad, Vinod Sci Rep Article We calculate the analytical and numerical values of the position space Shannon entropy, momentum space Shannon entropy, and total Shannon entropy, [Formula: see text] , [Formula: see text] , and [Formula: see text] , respectively, of free and trapped Rydberg hydrogen-like atoms. The influence of atomic number Z, the principal quantum number n, and energy E on the Shannon entropy of the Rydberg atoms are illustrated. The scaling properties of Shannon entropy with energy of states E and the principal quantum number n have been reported for the first time to the best of our knowledge. Our work explains how Shannon entropy indicates localization-delocalization of the wavefunction. The total Shannon entropy as a measure of the number of nodes in the trapped Rydberg atom’s wavefunction is also discussed. We show why an uncertainty relation based on Shannon entropy is superior to Heisenberg uncertainty for Rydberg atoms. Nature Publishing Group UK 2022-05-06 /pmc/articles/PMC9076694/ /pubmed/35523799 http://dx.doi.org/10.1038/s41598-022-10854-0 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 Kumar, Kirtee Prasad, Vinod Few generalized entropic relations related to Rydberg atoms |
title | Few generalized entropic relations related to Rydberg atoms |
title_full | Few generalized entropic relations related to Rydberg atoms |
title_fullStr | Few generalized entropic relations related to Rydberg atoms |
title_full_unstemmed | Few generalized entropic relations related to Rydberg atoms |
title_short | Few generalized entropic relations related to Rydberg atoms |
title_sort | few generalized entropic relations related to rydberg atoms |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9076694/ https://www.ncbi.nlm.nih.gov/pubmed/35523799 http://dx.doi.org/10.1038/s41598-022-10854-0 |
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