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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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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