Asymptotic Behavior of the Wave Packet Propagation through a Barrier:   the Green's Function Approach Revisited
  To model the decay of a quasibound state we use the modified two-potential approach introduced by Gurvitz and Kalbermann. This method has proved itself useful in the past for calculating the decay width and the energy shift of an isolated quasistationary state. We follow the same approach in order to propagate the wave-packet in time with the ultimate goal of extracting the momentum-distribution of emitted particles. The advantage of the method is that it provides the time-dependent wave function in a simple semi-analytic form. We intend to apply this method to the modeling of metastable states for which no direct integration of the time-dependent Schroedinger equation is available today. 
Bogdan Mihaila, Shmuel A. Gurvitz, David Dean, Witold Nazarewicz