Exact wave functions for generalized harmonic oscillators

Nathan Lanfear, Raquel M. López, Sergei Suslov

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)352-361
Number of pages10
JournalJournal of Russian Laser Research
Volume32
Issue number4
DOIs
StatePublished - Jul 1 2011

Keywords

  • Arnold transform
  • Ehrenfest theorem
  • Ermakov-type equation and Pinney-type solution
  • Green's function
  • dynamic invariant
  • generalized harmonic oscillators
  • time-dependent Schrödinger equation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering (miscellaneous)

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