  An effective operational approach to quantum mechanics is to focus on the
evolution of wave-packets, for which the wave-function can be seen in the
semi-classical regime as representing a classical motion dressed with extra
degrees of freedom describing the shape of the wave-packet and its
fluctuations. These quantum dressing are independent degrees of freedom,
mathematically encoded in the higher moments of the wave-function. We review
how to extract the effective dynamics for Gaussian wave-packets evolving
according to the Schrodinger equation with time-dependent potential in a
1+1-dimensional spacetime, and derive the equations of motion for the quadratic
uncertainty. We then show how to integrate the evolution of all the higher
moments for a general wave-function in a time-dependent harmonic potential.
