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Open Physics

Particle tunneling and scattering in a three-dimensional potential with a barrier

V. S. Olkhovsky, V. Petrillo, Jacek Jakiel, W. Kantor

Published Mar 1, 2008• 7 citations
Publisher

Abstract

Abstract The particle tunneling through a 3-D rectangular potential barrier has been studied. The simplest model for multiple internal reflections has been assumed. The explicit expression for all the transmission and reflection probability amplitudes have been derived, as well as the tunneling and reflection phase times.
DOI
10.2478/s11534-008-0071-8

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A non-stationary method for tunneling description of non-relativistic particles and photons through a barrier on the basis of consideration of the multiple internal reflections of vawe packets in relation of barrier boundaries is presented. The method is described in details and proved in the case of the one-dimentional tunneling of the particle through the rectangular barrier. For problems of the tunneling of the particle through the spherically symmetric barrier and of the photon through the one-dimensional barrier the amplitudes of transmitted and reflected wave packets in relation to the barrier, times of the tunneling and the reflection are found using of the method. Hartman's and Fletcher's effect is analysed.
The non-stationary solution method for a problem of tunneling of nonrelativistic particles and photons through a barrier on the basis of multiple internal re ections of wave packets in relation of barrier boundaries is submitted.The method is described and proved in solving an one-dimentional problem of tunneling of the particle through a rectangular barrier.For problems of tunneling of the particle through a spherically symmetric barrier and the photon through an one-dimensional barrier the amplitudes of transmitted and re ected wave packets in relation to the barrier, times of the tunneling and the re ection are found using of the method.Hartman's and Fletcher's eect is analysed.
The immersing method is used to solve the two-channel scattering problem in the case of concrete potential. In particular, we consider the particle scattering by a two-dimensional barrier which is constant in the scattering direction and is arbitrary in the transverse direction. For this case the scattering amplitudes t 1, t 2, r 1, and r 2 are determined. Expressions for the transmission and reflection amplitudes are obtained for the case of δ-potential. The behavior of the scattering amplitudes in the limit k 2 → 0 is studied. It is also shown that the ratio of products of transmission and reflection amplitudes for two channels does not depend on the coordinate of the middle of coordinate.