  The quantum Zakharov system is described in terms of a Lagrangian formalism.
A time-dependent Gaussian trial function approach for the envelope electric
field and the low-frequency part of the density fluctuation leads to a coupled,
nonlinear system of ordinary differential equations. In the semiclassic case,
linear stability analysis of this dynamical system shows a destabilizing r\^ole
played by quantum effects. Arbitrary value of the quantum effects are also
considered, yielding the ultimate destruction of the localized, Gaussian trial
solution. Numerical simulations are shown both for the semiclassic and the full
quantum cases.
