Surface oscillations and the surface thickness of classical and quantum droplets

We calculate the contribution from surface oscillations to the surface thickness of a liquid drop. The results are compared to those for a surface made plane by gravity. We find that the zero-point motion of the surface modes gives a contribution to the surface thickness which is independent of the drop radius R, and is in good agreement for liquid He4 with other estimates of the surface thickness. For classical droplets, the mean square displacement of the surface varies as log R, in accord with the plane surface results.