  The correspondence between classical and quantum invariants is established.
The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator
is translated from the coordinate and momentum operators into amplitude and
phase operators. In doing so, Turski's phase operator as well as
Susskind-Glogower operators are generalized to the time dependent harmonic
oscillator case. A quantum derivation of the Manley-Rowe relations is shown as
an example.
