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College Physics

The resarch on penetration coefficient in barrier penetration when ∪_0 =E

Yue Liu

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Formula for penetration coefficient in barrier penetration when ∪0-E is presented, and the question in the article 《The reserch on barrier of quantum mechanics from a piece of exercise》(《College Physics》 1993, 12(10)) is explained using this formula.

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‘‘Comment on ‘A study of barrier penetration in quantum mechanics’ by J. D. Chalk’’

Sean Washburn

American Journal of Physics•Aug 1, 1988•2 citations
A potential barrier of the kind studied by Fowler and others may be represented by the analytic function VVV (Eq. (1)). The Schr\"odinger equation associated to this potential is soluble in terms of hypergeometric functions, and the coefficient of reflection for electrons approaching the barrier with energy WWW is calculable (Eq. (15)). The approximate formula, $1\ensuremath{-}\ensuremath{\rho}=\mathrm{exp}{\ensuremath{-}\ensuremath{\int}\frac{4\ensuremath{\pi}}{h}{(2m(V\ensuremath{-}W))}^{\frac{1}{2}}\mathrm{dx}}$ is shown to agree very well with the exact formula when the width of the barrier is great compared to the de Broglie wave-length of the incident electron, and W<VmaxW<{V}_{max}W<Vmax​.