Application of Bound-State Solutions to the One-Dimensional Barrier Penetration Problem for Boltzmann Systems

Abstract

As an alternative to the conventional approach, it is proposed that the problem of Boltzmann particles impinging on an infinite one-dimensional potential barrier may be solved by making use of the bound-state solutions for the corresponding potential well. The method is shown to be rigorous for two simple barrier shapes, a parabolic barrier and a “double anharmonic” barrier; it is shown to be valid for the case of a general infinite barrier in the WKBJ approximation.