Exponential and non-exponential decay of an initially localized quantum state subject to two delta-barriers

Abstract

We study the time dependence of a quantum particle initially localized'behind two delta-function barriers of strengths v 1 and v 2 . We determine the conditions under which the decay is exponential by varying the ratio v 1 /v 2 and the separation between the delta-barriers. We find that exponential decay occurs even when v 1 /v 2 is of order one. We also find cases of non-exponential decay. An interesting example of non-exponential decay is when the two barriers are very close. We show that the exponential decay is due to poles in the complex k-plane, where k denotes the wave numbers of the energy eigenstates, and we find that the decay rates are fully understood in many cases as being due to a single pole.