Abstract
We investigate the Vlasov equation as a semiclassical approximation to quantum dynamics. The effect of the self-consistent mean field is modeled by a spatially fluctuating potential given in the form of randomly distributed Gaussians. The comparison of the quantum dynamics to its semiclassical approximation is done using the emittance of a wave packet as an observable. The analysis concentrates on the ħ→0 limit of TDHF by considering a representative test particle problem. We check a formal estimate of the quality of the semiclassical expansion against practical results. The quality of the semiclassical approach depends much on the observable of interest
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