Time development of a quasistationary state

Abstract

Approximately 40 years ago it was realized that the time development of decaying systems might not be precisely exponential. Winter [Phys. Rev. 123, 1503 (1961)] analyzed the simplest nontrivial system---a particle tunneling out of a well formed by a wall and $\ensuremath{\delta}$ function. He calculated the probability current just outside the well and found irregular oscillations on a short-time scale followed by an exponential decrease followed by more oscillations and finally by a decrease as a power of the time. We have reanalyzed this system, concentrating on the survival probability of the particle in the well rather than the probability current, and find a different short-time behavior.