  We show that Liouville-von Neumann approach to quantum mechanical systems,
which demands the existence of invariant operators, reproduces the
time-dependent variational Gaussian approximation. We find the effective action
of the time-dependent systems and show that many aspects of the dynamics are
independent of the details of time evolution, e.g., the squeezing of the
wave-function is determined by the effective potential of the final stage of
time-evolution.
