  By adapting the Madelung-Bohm formalism to paraxial wave propagation we show,
by using Ermakov-Lewis techniques, that the Gouy phase is related to the form
of the phase chosen in order to produce a Gaussian function as a propagated
field. For this, we introduce a quantum mechanical invariant, that it is
explicitly time dependent despite the fact that the Hamiltonian is itself
time-independent. We finally show that the effective Bohm {\it index of
refraction} generates a GRIN medium that produces the focusing needed for the
Gouy phase.
