Reflection of particles by one-dimensional potential barriers of arbitrary shape

V.V. Babikov, K. K. Musabaev

Er-juan Bai, Shu Qi-Qing

For a one-dimensional barrier of arbitrary shape, an expression of the dwell time of tunneling particles has been obtained by subdividing it into infinitesimal rectangular barrier elements and then summing the dwell times spent by particles inside the barrier elements, and the dwell times in a parabolic potential barrier were calculated. The results show that the dwell times are almost independent of the barrier width as it is greater than a characteristic width W c . This can be ascribed that in the width range beyond W c , the tunneling probabilities through the barrier elements are very small, thus the times taken to tunnel through them make little contribution to the summation of the dwell times in all the barrier elements.

Leonid D. Shvartsman, Dmitri Romanov, J. E. Golub

Motivated by the behavior of carriers in various condensed systems, we formulate and discuss the mechanics of a particle described by a nonmonotonic dispersion law. For illustration, we consider the scattering of a particle with a @sw-shaped dispersion law by a one-dimensional potential barrier. The negative mass feature of the dispersion gives rise to a number of unusual phenomena, including barrier penetration by a classical particle, particle trapping by the barrier, and scattering resonances in both transmission and reflection.

Lyudvig Dmitrievich Faddeev, O. Yakubovskiĭ

Örjan Dammert

A smooth one-dimensional system of N potential barriers of arbitrary shapes (unequal or equal) is considered. A general necessary condition for complete transparency is obtained that can be understood as a constraint on the reflection coefficients pertaining to the single barriers of the system. A maximum transmission problem of a general kind is solved and the solution is used to give a physical interpretation of the necessary condition. The sub- and superbarrier cases are treated in a unified way. The exact final formulas can readily be converted into accurate approximate ones by insertion of available phase-integral expressions (of an arbitrary order) for certain characteristic quantities appearing in the formulas.

Florian A. Scheck