Exact wave functions for generalized harmonic oscillators

We transform the time-dependent Schrödinger 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 the solutions of certain Ermakov and Riccatitype systems. In addition, we show that the classical Arnold transform is naturally connected with Ehrenfest’s theorem for generalized harmonic oscillators.