2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89626We consider the evolution of Green's function of the one-dimensional Schrödinger 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.8 pages, no figures, we would welcome commentsQuantum Physicstext