Total Absorption in Finite Time in an iδ Potential
Abstract
We consider the evolution of Green's function of the one-dimensional Schr\"odinger equation in the presence of the complex potential -ikδ(x). Our result is the construction of an explicit time-dependent solution which we use to calculate the time-dependent survival probability of a quantum particle. The survival probability decays to zero in finite time, which means that the complex delta potential well is a total absorber for quantum particles. This potential can be interpreted as a killing measure with infinite killing rate concentrated at the origin.
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