  We consider the evolution of Green's function of the one-dimensional
Schr\"odinger equation in the presence of the complex potential $-ik\delta(x)$.
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.
