Dynamical invariants for variable quadratic Hamiltonians

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27 Scopus citations


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
Issue number5
StatePublished - 2010

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics
  • Physics and Astronomy(all)


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