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

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