  The Ermakov Lewis quantum invariant for the time dependent harmonic
oscillator is expressed in terms of number and phase operators. The
identification of these variables is made in accordance with the correspondence
principle and the amplitude and phase representation of the classical
orthogonal functions invariant. The relationship between the number and phase
operators is established through this invariant as the system evolves from one
frequency to another. In the specific case where the excitations represent the
photon number, these relations are equivalent to the power density transport
equations derived in nonlinear optical processes.
