One-dimensional diffusion through single- and double-square barriers

Abstract

Exact solutions are obtained for the diffusion through single- and double-square potentials, by using the Laplace transform method. We compare transmission of a classical particle through one barrier of given length and through two barriers with a well between them of the same overall length. The influence of the barriers' heights and widths as well as of the distances to the reflecting walls is studied in detail. The results obtained are used to estimate the limits of applicability of the Kramers rate theory.