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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Autores principales:	A.-V. Phan, M. Karimaghaei
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Quantum billiards Energy eigenvalues Free-particle Green’s function Boundary integral method Mechanics of engineering. Applied mechanics TA349-359 Technology T
Acceso en línea:	https://doaj.org/article/a1fa66fe50eb42e685a577296f122dc6
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spelling	oai:doaj.org-article:a1fa66fe50eb42e685a577296f122dc62021-11-18T04:51:54ZA standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis2666-359710.1016/j.finmec.2021.100027https://doaj.org/article/a1fa66fe50eb42e685a577296f122dc62021-10-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666359721000184https://doaj.org/toc/2666-3597By 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.A.-V. PhanM. KarimaghaeiElsevierarticleQuantum billiardsEnergy eigenvaluesFree-particle Green’s functionBoundary integral methodMechanics of engineering. Applied mechanicsTA349-359TechnologyTENForces in Mechanics, Vol 4, Iss , Pp 100027- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Quantum billiards Energy eigenvalues Free-particle Green’s function Boundary integral method Mechanics of engineering. Applied mechanics TA349-359 Technology T
spellingShingle	Quantum billiards Energy eigenvalues Free-particle Green’s function Boundary integral method Mechanics of engineering. Applied mechanics TA349-359 Technology T A.-V. Phan M. Karimaghaei A standard energy eigenvalue problem for directly solving the stationary states of quantum billiards via boundary integral analysis
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.
format	article
author	A.-V. Phan M. Karimaghaei
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
publishDate	2021
url	https://doaj.org/article/a1fa66fe50eb42e685a577296f122dc6
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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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