Transition-state theory for quantum and classical particle escape from a finite square well

Abstract

A precise statement of transition-state theory is given. The theory is made intuitive and precise by the introduction of a ‘‘semipermeable’’ barrier between reactant and product. The theory is then illustrated by calculating, both quantum and classical mechanically, the rate of particle escape from a finite square well. The two calculations are fundamentally different and illuminate different aspects of the theory. Finally, the solution is recast into the Arrhenian form with which it is usually identified, and physically satisfying expressions for the rate prefactor, activation energy, and activation entropy are obtained.