Exact Wave Functions for Generalized Harmonic Oscillators
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2011
- DOI:
- 10.48550/arXiv.1102.5119
- arXiv:
- arXiv:1102.5119
- Bibcode:
- 2011arXiv1102.5119L
- Keywords:
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- Mathematical Physics
- E-Print:
- 10 pages, no figures