Collapse of wave functions in Schrödinger's wave mechanics

We show that inelastic scattering in a short-range potential leads to a collapse of the wave function within standard evolution through the Schrödinger equation, whereas elastic scattering will not collapse the wave function. Specifically, we find that the initial width of the emerging wave function in inelastic scattering is primarily determined by the size of the participating scattering center and the range of the scattering potential, but not by the width of the incoming wave function. This indicates that dynamical collapse of the wave function through inelastic scattering can explain the emergence of particle-like signals.