Time Evolution of a Decaying Quantum State: Evaluation and Onset of Non-Exponential Decay

Abstract

The method developed by Van Dijk, Nogami and Toyama for obtaining the time-evolved wave function of a decaying quantum system is generalized to potentials and initial wave functions of non-compact support. The long time asymptotic behavior is extracted and employed to predict the timescale for the onset of non-exponential decay. The method is illustrated with a Gaussian initial wave function leaking through Eckart's potential barrier on the halfline.