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We follow the emergence of quantum entanglement in a scattering event betweentwo initially uncorrelated distinguishable quantum particles interacting via adelta potential. We calculate the time dependence of the Neumann entropy of theone-particle reduced density matrix. By using the exact propagator for thedelta potential, we derive an approximate analytic formula for the asymptoticform of the two-particle wave function which is sufficiently accurate toaccount for the entanglement features of the system.

Time dependence of quantum entanglement in the collision of two particles