Exploiting Modern Chladni Plates to Analogously Manifest the Point Interaction

A truncated basis is employed to analyze the influence of the point interaction on the eigenvalues and eigenfunctions in quantum billiards. The point interaction is numerically confirmed to cause the shift in the eigenvalue that leads the original eigenfunctions to be superposed to form the new eige...

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Autores principales:	Yu-Chen Tseng, Yu-Hsin Hsu, Yu-Hsiang Lai, Yan-Ting Yu, Hsing-Chih Liang, Kai-Feng Huang, Yung-Fu Chen
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	point interaction quantum billiards Chladni plates Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/372c53d5b1524cc9970c2c22acaa18ef
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id	oai:doaj.org-article:372c53d5b1524cc9970c2c22acaa18ef
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spelling	oai:doaj.org-article:372c53d5b1524cc9970c2c22acaa18ef2021-11-11T15:09:49ZExploiting Modern Chladni Plates to Analogously Manifest the Point Interaction10.3390/app1121100942076-3417https://doaj.org/article/372c53d5b1524cc9970c2c22acaa18ef2021-10-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/21/10094https://doaj.org/toc/2076-3417A truncated basis is employed to analyze the influence of the point interaction on the eigenvalues and eigenfunctions in quantum billiards. The point interaction is numerically confirmed to cause the shift in the eigenvalue that leads the original eigenfunctions to be superposed to form the new eigenfunction. The amplitude and nodal-line patterns of the eigenfunctions are found to vary significantly with the coupling strength. It is further verified that the point-driven Chladni plates can be employed to analogously manifest the noticeable dependence of the nodal-line pattern on the coupling strength. More importantly, the dispersion relation between the frequency and the wave number for the flexural wave can be precisely determined in the process of utilizing the point interaction to model the modern Chladni plates.Yu-Chen TsengYu-Hsin HsuYu-Hsiang LaiYan-Ting YuHsing-Chih LiangKai-Feng HuangYung-Fu ChenMDPI AGarticlepoint interactionquantum billiardsChladni platesTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10094, p 10094 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	point interaction quantum billiards Chladni plates Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	point interaction quantum billiards Chladni plates Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Yu-Chen Tseng Yu-Hsin Hsu Yu-Hsiang Lai Yan-Ting Yu Hsing-Chih Liang Kai-Feng Huang Yung-Fu Chen Exploiting Modern Chladni Plates to Analogously Manifest the Point Interaction
description	A truncated basis is employed to analyze the influence of the point interaction on the eigenvalues and eigenfunctions in quantum billiards. The point interaction is numerically confirmed to cause the shift in the eigenvalue that leads the original eigenfunctions to be superposed to form the new eigenfunction. The amplitude and nodal-line patterns of the eigenfunctions are found to vary significantly with the coupling strength. It is further verified that the point-driven Chladni plates can be employed to analogously manifest the noticeable dependence of the nodal-line pattern on the coupling strength. More importantly, the dispersion relation between the frequency and the wave number for the flexural wave can be precisely determined in the process of utilizing the point interaction to model the modern Chladni plates.
format	article
author	Yu-Chen Tseng Yu-Hsin Hsu Yu-Hsiang Lai Yan-Ting Yu Hsing-Chih Liang Kai-Feng Huang Yung-Fu Chen
author_facet	Yu-Chen Tseng Yu-Hsin Hsu Yu-Hsiang Lai Yan-Ting Yu Hsing-Chih Liang Kai-Feng Huang Yung-Fu Chen
author_sort	Yu-Chen Tseng
title	Exploiting Modern Chladni Plates to Analogously Manifest the Point Interaction
title_short	Exploiting Modern Chladni Plates to Analogously Manifest the Point Interaction
title_full	Exploiting Modern Chladni Plates to Analogously Manifest the Point Interaction
title_fullStr	Exploiting Modern Chladni Plates to Analogously Manifest the Point Interaction
title_full_unstemmed	Exploiting Modern Chladni Plates to Analogously Manifest the Point Interaction
title_sort	exploiting modern chladni plates to analogously manifest the point interaction
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/372c53d5b1524cc9970c2c22acaa18ef
work_keys_str_mv	AT yuchentseng exploitingmodernchladniplatestoanalogouslymanifestthepointinteraction AT yuhsinhsu exploitingmodernchladniplatestoanalogouslymanifestthepointinteraction AT yuhsianglai exploitingmodernchladniplatestoanalogouslymanifestthepointinteraction AT yantingyu exploitingmodernchladniplatestoanalogouslymanifestthepointinteraction AT hsingchihliang exploitingmodernchladniplatestoanalogouslymanifestthepointinteraction AT kaifenghuang exploitingmodernchladniplatestoanalogouslymanifestthepointinteraction AT yungfuchen exploitingmodernchladniplatestoanalogouslymanifestthepointinteraction
_version_	1718437123608018944

Exploiting Modern Chladni Plates to Analogously Manifest the Point Interaction

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