Evolution of a Quasi-Stationary State

To elucidate the time development of quasi-stationary states, a simple barrier penetration problem has been studied. Both approximate expressions and numerical results for some parameters were obtained for the decay rate. First, irregular oscillations occur for a short time. Second, the exponential region follows. Third, further oscillations occur during which the decay rate dips to negative values, so that the probability of finding the undecayed system increases briefly at several times. Fourth and finally, the decay rate decreases like an inverse power of the time.