Exact Wave Functions for Generalized Harmonic Oscillators
  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. 
Nathan Lanfear, Raquel M. Lopez and Sergei K. Suslov
math-ph math.MP