COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVEL

In this work, a simple derivation of the variable amplitude method using the variation of parameters to solve a differential equation is presented. The variable amplitude method was originally devised by Tikochinsky in 1977, using the quantum theory of scattering. The method is applied to two model...

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Main Authors: Éderson D'M. Costa, Luciano Cordeiro, Nelson H. T. Lemes, João P. Braga
Format: Article
Language:English
Published: Sociedade Brasileira de Química
Series:Química Nova
Subjects:
Online Access:http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-40422016000700882&lng=en&tlng=en
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spelling doaj-2a2734f0bf55432585fe2a3494eec07e2020-11-24T21:11:55ZengSociedade Brasileira de QuímicaQuímica Nova1678-706439788288510.5935/0100-4042.20160061S0100-40422016000700882COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVELÉderson D'M. CostaLuciano CordeiroNelson H. T. LemesJoão P. BragaIn this work, a simple derivation of the variable amplitude method using the variation of parameters to solve a differential equation is presented. The variable amplitude method was originally devised by Tikochinsky in 1977, using the quantum theory of scattering. The method is applied to two model potentials, the rectangular potential barrier and the Eckart potential, both with analytical solutions for the reflection coefficient. Numerical results will be compared with the exact values for several energies. The problem of calculating the reflection coefficient, usually involving extensive algebra as described in several textbooks, is reduced to solving a first order differential equation with initial condition. The method is very simple to apply, representing an attractive tool for teaching introductory quantum mechanics. A simple computer code is available from which reflection coefficients for the Eckart potential can be calculated.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-40422016000700882&lng=en&tlng=entransmission coefficientquantum tunnelingvariation of parameters
collection DOAJ
language English
format Article
sources DOAJ
author Éderson D'M. Costa
Luciano Cordeiro
Nelson H. T. Lemes
João P. Braga
spellingShingle Éderson D'M. Costa
Luciano Cordeiro
Nelson H. T. Lemes
João P. Braga
COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVEL
Química Nova
transmission coefficient
quantum tunneling
variation of parameters
author_facet Éderson D'M. Costa
Luciano Cordeiro
Nelson H. T. Lemes
João P. Braga
author_sort Éderson D'M. Costa
title COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVEL
title_short COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVEL
title_full COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVEL
title_fullStr COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVEL
title_full_unstemmed COEFICIENTES DE TRANSMISSÃO E REFLEXÃO PELO MÉTODO DA AMPLITUDE VARIÁVEL
title_sort coeficientes de transmissão e reflexão pelo método da amplitude variável
publisher Sociedade Brasileira de Química
series Química Nova
issn 1678-7064
description In this work, a simple derivation of the variable amplitude method using the variation of parameters to solve a differential equation is presented. The variable amplitude method was originally devised by Tikochinsky in 1977, using the quantum theory of scattering. The method is applied to two model potentials, the rectangular potential barrier and the Eckart potential, both with analytical solutions for the reflection coefficient. Numerical results will be compared with the exact values for several energies. The problem of calculating the reflection coefficient, usually involving extensive algebra as described in several textbooks, is reduced to solving a first order differential equation with initial condition. The method is very simple to apply, representing an attractive tool for teaching introductory quantum mechanics. A simple computer code is available from which reflection coefficients for the Eckart potential can be calculated.
topic transmission coefficient
quantum tunneling
variation of parameters
url http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-40422016000700882&lng=en&tlng=en
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AT nelsonhtlemes coeficientesdetransmissaoereflexaopelometododaamplitudevariavel
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