One-dimensional δ-function potential and the radiation boundary condition

We discuss two different representations of a single imperfect trap in one dimension, a δ-function potential in a Schrödinger-like reaction-diffusion equation, and the classical radiation boundary condition description. In the context of self-segregation in trapping problems, we show explicitly the equivalence of the models under certain conditions, and discuss the general differences. We also point out the applicability of both models for various physical systems.