Novel approach to tunneling problems

Abstract

We consider a tunneling problem as the decay of a prepared state using a modified two-potential approach. This method enables us to obtain a perturbative expansion for the decay width and the energy shift of an isolated quasistationary state. The first term is very simple and the correction terms are found to be small. Some examples for application of our result are presented. The quasi- classical limit of the width \ensuremath{\Gamma} has the form of the Gamow formula, but with a well-defined prefactor valid also for low-lying states. This result coincides with that of instanton calculations in the limit of \ensuremath{\Elzxh}\ensuremath{\rightarrow}0.