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Acta Physica Sinica

Transmission resonance for a Klein-Gordon particle in one-dimensional Hulthén potential barrier

Min‐Cang Zhang, 陕西师范大学物理学与信息技术学院,西安 710062

Published Jan 1, 2009• 0 citations
Publisher

Abstract

The Klein-Gordon equation in the presence of a spatially one-dimensional Hulthén potential barrier is solved and the scattering state solutions are obtained in terms of the hypergeometric functions. Both the reflection coefficient and transmission coefficient are calculated from the boundary condition of Klein-Gordon equation and the conditions for transmission resonance are then derived.The result shows that when the reflection coefficient is zero the transmission resonance takes place.

DOI
10.7498/aps.58.5961

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The Klein-Gordon equation in the presence of a spatially one-dimensional Hulthén potential barrier is solved and the scattering state solutions are obtained in terms of the hypergeometric functions. Both the reflection coefficient and transmission coefficient are calculated from the boundary condition of Klein-Gordon equation and the conditions for transmission resonance are then derived.The result shows that when the reflection coefficient is zero the transmission resonance takes place.
Abstract We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthén potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have derived the reflection and transmission coefficients using the matching condition on the wavefunctions, and investigated the condition for the existence of transmission resonance. Furthermore, we have demonstrated how the transmission resonance depends on the shape of the potential.
We have solved exactly the two-component Dirac equation in the presence of a spatially one-dimensional Hulthén potential, and presented the Dirac spinors of scattering states in terms of hypergeometric functions. We have calculated the reflection and transmission coefficients by the matching conditions on the wavefunctions, and investigated the condition for the existence of transmission resonances. Furthermore, we have demonstrated how the transmission-resonance condition depends on the shape of the potential.