Evolution of the wave-function’s shape in a time-dependent harmonic potential

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