  We follow the emergence of quantum entanglement in a scattering event between
two initially uncorrelated distinguishable quantum particles interacting via a
delta potential. We calculate the time dependence of the Neumann entropy of the
one-particle reduced density matrix. By using the exact propagator for the
delta potential, we derive an approximate analytic formula for the asymptotic
form of the two-particle wave function which is sufficiently accurate to
account for the entanglement features of the system.
