A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis

By using the series expansions of the Bessel functions for the real and imaginary parts of the free particle Green’s function for the two-dimensional stationary states of quantum billiards, it can be shown that some components of the Green’s function are redundant which can be eliminated to make the...

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Main Authors:	A.-V. Phan, M. Karimaghaei
Format:	Article
Language:	English
Published:	Elsevier 2021-10-01
Series:	Forces in Mechanics
Subjects:	Quantum billiards Energy eigenvalues Free-particle Green’s function Boundary integral method
Online Access:	http://www.sciencedirect.com/science/article/pii/S2666359721000184

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spelling	doaj-a1fa66fe50eb42e685a577296f122dc62021-06-15T04:15:19ZengElsevierForces in Mechanics2666-35972021-10-014100027A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysisA.-V. Phan0M. Karimaghaei1Corresponding author.; Department of Mechanical, Aerospace and Biomedical Engineering, University of South Alabama,Mobile, AL 36688, USADepartment of Mechanical, Aerospace and Biomedical Engineering, University of South Alabama,Mobile, AL 36688, USABy using the series expansions of the Bessel functions for the real and imaginary parts of the free particle Green’s function for the two-dimensional stationary states of quantum billiards, it can be shown that some components of the Green’s function are redundant which can be eliminated to make the boundary integral equation for the wave function of free particles inside quantum billiards independent of the wave numbers. This development leads to a much faster search for the energy eigenvalues of quantum billiards by scanning their wave numbers or the formulation of the standard eigenvalue problem which can directly be solved for the energy eigenvalues. Some numerical examples were used to demonstrate that the proposed technique is accurate, computationally effective and straightforward to be applied in practice.http://www.sciencedirect.com/science/article/pii/S2666359721000184Quantum billiardsEnergy eigenvaluesFree-particle Green’s functionBoundary integral method
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	A.-V. Phan M. Karimaghaei
spellingShingle	A.-V. Phan M. Karimaghaei A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis Forces in Mechanics Quantum billiards Energy eigenvalues Free-particle Green’s function Boundary integral method
author_facet	A.-V. Phan M. Karimaghaei
author_sort	A.-V. Phan
title	A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis
title_short	A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis
title_full	A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis
title_fullStr	A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis
title_full_unstemmed	A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis
title_sort	standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis
publisher	Elsevier
series	Forces in Mechanics
issn	2666-3597
publishDate	2021-10-01
description	By using the series expansions of the Bessel functions for the real and imaginary parts of the free particle Green’s function for the two-dimensional stationary states of quantum billiards, it can be shown that some components of the Green’s function are redundant which can be eliminated to make the boundary integral equation for the wave function of free particles inside quantum billiards independent of the wave numbers. This development leads to a much faster search for the energy eigenvalues of quantum billiards by scanning their wave numbers or the formulation of the standard eigenvalue problem which can directly be solved for the energy eigenvalues. Some numerical examples were used to demonstrate that the proposed technique is accurate, computationally effective and straightforward to be applied in practice.
topic	Quantum billiards Energy eigenvalues Free-particle Green’s function Boundary integral method
url	http://www.sciencedirect.com/science/article/pii/S2666359721000184
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A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis

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