On a Rigorous Proof of the Joos-Zeh Formula for Decoherence in a Two-Body Problem

We consider a simple one dimensional system consisting of two particles interacting with a $\delta$-potential and we discuss a rigorous derivation of the asymptotic wave function of the system in the limit of small mass ratio. We apply the result to the explicit computation of the decoherence effect induced by scattering in a concrete example of quantum evolution.