Finite square well with a time varying distortion: Application of the Wei-Norman Factorization

Abstract

We consider a particle initially trapped inside a finite square well. The system experiences a linear distorting potential which creates an effective barrier for the particle to tunnel. We want to know the state of the particle just before the tunneling occurs. In this paper we provide a scheme of how to solve the problem using the Lie algebraic approach of Wei and Norman. We also show that the chosen representation yields a time evolution operator that is global in time. Numerical evolution of the particle’s state is also outlined.