Deviations from exponential decay in quantum mechanics

Abstract

The usual quantum mechanical explanation of exponential decay is not exact. The approximations made lead to an average lifetime which can also be obtained directly using Fermi's Golden Rule. The question whether or not quantum mechanical decay is always exponential was recently raised again in connection with the possible decay of the proton. In this paper we derive a new criterion for the length of the non-exponential decay era. A formalism for general quantum systems is used to derive an exact expression for the survival probability in terms of a spectral density function. This expression is used for numerical studies. We find that in general, for short times, the decay is not exponential. In some cases a quadratic law is followed instead.