Abstract
The most consistent way of describing the scattering process would be to follow the time evolution of the particle wave function, starting with a certain initial form of it. This initial form corresponds to a particle localized at a given time in the source far from the target. The time evolution of the wave function is governed by the Schrodinger equation $$i\hat n\frac{{\partial \psi }}{{\partial t}} = H\psi $$
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