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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...

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Autores principales: Kumar, Kirtee, Prasad, Vinod
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2022
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
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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.
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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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