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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.

Keywords

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

R2 v1 2026-06-21T17:31:28.884Z