Dynamical invariants for variable quadratic Hamiltonians

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schrödinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

Original languageEnglish (US)
Article number055006
JournalPhysica Scripta
Volume81
Issue number5
DOIs
StatePublished - May 24 2010

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics

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