  This paper proves the validity of the joint mean-field and classical limit of
the quantum $N$-body dynamics leading to the pressureless Euler-Poisson system
for factorized initial data whose first marginal has a monokinetic Wigner
measure. The interaction potential is assumed to be the repulsive Coulomb
potential. The validity of this derivation is limited to finite time intervals
on which the Euler-Poisson system has a smooth solution that is rapidly
decaying at infinity. One key ingredient in the proof is an inequality from [S.
Serfaty, with an appendix of M. Duerinckx arXiv:1803.08345v3 [math.AP]].
