Exact Wave Functions for Generalized Harmonic Oscillators

Details Exact Wave Functions for Generalized Harmonic Oscillators Exact Wave Functions for Generalized Harmonic Oscillators

2011-02-24

arxiv.org/abs/1102.5119v2

Physics

Mathematical Physics

10 pages, no figures

Scientific paper

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.

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