This article describes some recent experiments which demonstrate pheno
mena, in both superfluid He-4 and He-3, that can easily be interpreted
in terms of the quantum phase dynamics approach of the Josephson-Ande
rson (JA) equation. In one experiment, a quantized vortex filament per
forms a stable precession in a cylinder at a frequency given by the JA
equation. In other experiments, superflow in submicron apertures exhi
bits discrete phase slips whose magnitude is quantized in units given
by the JA equation. These discrete phase slips provide information on
the nucleation processes which lead to the creation of quantized vorti
city.