Exact Wave Functions for Generalized Harmonic Oscillators
Mathematical Physics
2011-07-21 v2 math.MP
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.
Cite
@article{arxiv.1102.5119,
title = {Exact Wave Functions for Generalized Harmonic Oscillators},
author = {Nathan Lanfear and Raquel M. Lopez and Sergei K. Suslov},
journal= {arXiv preprint arXiv:1102.5119},
year = {2011}
}
Comments
10 pages, no figures