  We transform the time-dependent Schroedinger equation for the most general
variable quadratic Hamiltonians into a standard autonomous form. As a result,
the time-evolution of exact wave functions of generalized harmonic oscillators
is determined in terms of solutions of certain Ermakov and Riccati-type
systems. In addition, we show that the classical Arnold transformation is
naturally connected with Ehrenfest's theorem for generalized harmonic
oscillators.
