Exact wave functions for generalized harmonic oscillators

Nathan Lanfear, Raquel M. López, Sergei Suslov

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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
Issue number4
StatePublished - Jul 2011


  • 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)


Dive into the research topics of 'Exact wave functions for generalized harmonic oscillators'. Together they form a unique fingerprint.

Cite this