Using the time-dependent wave-packets method, we have quantum mechanically investigated the three-body recombination process for electron energies varying from 10 to 0.01 eV. The classical "bottleneck" prediction on the probable population was confirmed by our S-wave quantum calculations for electron kinetic energies (K(E)) as low as 0.1 eV. But for K(E)<0.1 eV, the quantum three-body recombination tends to populate lower n levels than the classical theory predicted. We also find that, in the same n level, the recombination tends to populate higher angular-momentum states with K(E) decreasing. These results may shed light on the intrinsic dynamics of both ultracold plasmas and frozen Rydberg gases.