Algorithms for Non-Relativistic Quantum Integral Equation

Detalhes bibliográficos
Autor(a) principal: Sales, Jorge Henrique de Oliveira
Data de Publicação: 2021
Outros Autores: Girotto, Pedro Henrique Sales
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Revista de Engenharia Química e Química
Texto Completo: https://periodicos.ufv.br/jcec/article/view/12699
Resumo: In low energy scattering in Non-Relativistic Quantum Mechanics, the Schödinger equation in integral form is used. In quantum scattering theory the wave self-function is divided into two parts, one for the free wave associated with the particle incident to a scattering center, and the emerging wave that comes out after the particle collides with the scattering center. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. The methods used here are arbitrary kernels and the Neumann-Born series. The result, with the help of computational codes, shows that both techniques are good compared to the traditional method. The advantage is that they are finite solutions, which does not require Podolsky-type regularization.
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spelling Algorithms for Non-Relativistic Quantum Integral EquationAlgoritmos para Equação Integral Quântico Não RelativísticoQuantum scattering. Fredholm. Neumann-Born. Computational modeling.Espalhamento quântico. Fredholm. Neumann-Born. Modelagem computacional.In low energy scattering in Non-Relativistic Quantum Mechanics, the Schödinger equation in integral form is used. In quantum scattering theory the wave self-function is divided into two parts, one for the free wave associated with the particle incident to a scattering center, and the emerging wave that comes out after the particle collides with the scattering center. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. The methods used here are arbitrary kernels and the Neumann-Born series. The result, with the help of computational codes, shows that both techniques are good compared to the traditional method. The advantage is that they are finite solutions, which does not require Podolsky-type regularization.No espalhamento a baixa energia na Mecânica Quântica não Relativística, usa-se aequação de Schödinger na forma integral. Na teoria do espalhamento quântico a autofunção de onda é dividida em duas partes, uma para a onda livre associada a partícula incidente àum centro espalhador, e a onda emergente que sai depois da partícula colidir com o centroespalhador. Admitindo que o centro espalhador contém um potencial dependente da posição, a solução usual da equação integral para a onda espalhada é obtida via aproximação de Born. Neste artigo apresenta-se duas técnicas alternativas para solução da equação integral contendo um potencial eletrostático. Os métodos usados aqui, são Kerneis arbitrários e a série de Neumann-Born. O resultado, com a ajuda de códigos computacionais, mostra que as duas técnicas são boas comparadas com o método tradicional. A vantagem é que são soluções finitas, que não requer regularização do tipo Podolsky.Universidade Federal de Viçosa - UFV2021-07-26info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.ufv.br/jcec/article/view/1269910.18540/jcecvl7iss3pp12699-01-19eThe Journal of Engineering and Exact Sciences; Vol. 7 No. 3 (2021); 12699-01-19eThe Journal of Engineering and Exact Sciences; Vol. 7 Núm. 3 (2021); 12699-01-19eThe Journal of Engineering and Exact Sciences; v. 7 n. 3 (2021); 12699-01-19e2527-1075reponame:Revista de Engenharia Química e Químicainstname:Universidade Federal de Viçosa (UFV)instacron:UFVenghttps://periodicos.ufv.br/jcec/article/view/12699/6776Copyright (c) 2021 The Journal of Engineering and Exact Scienceshttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessSales, Jorge Henrique de Oliveira Girotto, Pedro Henrique Sales2021-08-16T18:50:11Zoai:ojs.periodicos.ufv.br:article/12699Revistahttp://www.seer.ufv.br/seer/rbeq2/index.php/req2/indexONGhttps://periodicos.ufv.br/jcec/oaijcec.journal@ufv.br||req2@ufv.br2446-94162446-9416opendoar:2021-08-16T18:50:11Revista de Engenharia Química e Química - Universidade Federal de Viçosa (UFV)false
dc.title.none.fl_str_mv Algorithms for Non-Relativistic Quantum Integral Equation
Algoritmos para Equação Integral Quântico Não Relativístico
title Algorithms for Non-Relativistic Quantum Integral Equation
spellingShingle Algorithms for Non-Relativistic Quantum Integral Equation
Sales, Jorge Henrique de Oliveira
Quantum scattering. Fredholm. Neumann-Born. Computational modeling.
Espalhamento quântico. Fredholm. Neumann-Born. Modelagem computacional.
title_short Algorithms for Non-Relativistic Quantum Integral Equation
title_full Algorithms for Non-Relativistic Quantum Integral Equation
title_fullStr Algorithms for Non-Relativistic Quantum Integral Equation
title_full_unstemmed Algorithms for Non-Relativistic Quantum Integral Equation
title_sort Algorithms for Non-Relativistic Quantum Integral Equation
author Sales, Jorge Henrique de Oliveira
author_facet Sales, Jorge Henrique de Oliveira
Girotto, Pedro Henrique Sales
author_role author
author2 Girotto, Pedro Henrique Sales
author2_role author
dc.contributor.author.fl_str_mv Sales, Jorge Henrique de Oliveira
Girotto, Pedro Henrique Sales
dc.subject.por.fl_str_mv Quantum scattering. Fredholm. Neumann-Born. Computational modeling.
Espalhamento quântico. Fredholm. Neumann-Born. Modelagem computacional.
topic Quantum scattering. Fredholm. Neumann-Born. Computational modeling.
Espalhamento quântico. Fredholm. Neumann-Born. Modelagem computacional.
description In low energy scattering in Non-Relativistic Quantum Mechanics, the Schödinger equation in integral form is used. In quantum scattering theory the wave self-function is divided into two parts, one for the free wave associated with the particle incident to a scattering center, and the emerging wave that comes out after the particle collides with the scattering center. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. Assuming that the scattering center contains a position-dependent potential, the usual solution of the integral equation for the scattered wave is obtained via the Born approximation. The methods used here are arbitrary kernels and the Neumann-Born series. The result, with the help of computational codes, shows that both techniques are good compared to the traditional method. The advantage is that they are finite solutions, which does not require Podolsky-type regularization.
publishDate 2021
dc.date.none.fl_str_mv 2021-07-26
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.ufv.br/jcec/article/view/12699
10.18540/jcecvl7iss3pp12699-01-19e
url https://periodicos.ufv.br/jcec/article/view/12699
identifier_str_mv 10.18540/jcecvl7iss3pp12699-01-19e
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://periodicos.ufv.br/jcec/article/view/12699/6776
dc.rights.driver.fl_str_mv Copyright (c) 2021 The Journal of Engineering and Exact Sciences
https://creativecommons.org/licenses/by/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2021 The Journal of Engineering and Exact Sciences
https://creativecommons.org/licenses/by/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Viçosa - UFV
publisher.none.fl_str_mv Universidade Federal de Viçosa - UFV
dc.source.none.fl_str_mv The Journal of Engineering and Exact Sciences; Vol. 7 No. 3 (2021); 12699-01-19e
The Journal of Engineering and Exact Sciences; Vol. 7 Núm. 3 (2021); 12699-01-19e
The Journal of Engineering and Exact Sciences; v. 7 n. 3 (2021); 12699-01-19e
2527-1075
reponame:Revista de Engenharia Química e Química
instname:Universidade Federal de Viçosa (UFV)
instacron:UFV
instname_str Universidade Federal de Viçosa (UFV)
instacron_str UFV
institution UFV
reponame_str Revista de Engenharia Química e Química
collection Revista de Engenharia Química e Química
repository.name.fl_str_mv Revista de Engenharia Química e Química - Universidade Federal de Viçosa (UFV)
repository.mail.fl_str_mv jcec.journal@ufv.br||req2@ufv.br
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