Total Absorption in Finite Time in an $iδ$ Potential
Abstract
Description
We 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 comments
8 pages, no figures, we would welcome comments