Quantum integrals of motion for variable quadratic Hamiltonians

Ricardo Cordero-Soto, Erwin Suazo, Sergei Suslov

Research output: Contribution to journalArticle

38 Scopus citations

Abstract

We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schrödinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

Original languageEnglish (US)
Pages (from-to)1884-1912
Number of pages29
JournalAnnals of Physics
Volume325
Issue number9
DOIs
StatePublished - Sep 1 2010

Keywords

  • Caldirola-Kanai Hamiltonians
  • Cauchy initial value problem
  • Ehrenfest's theorem
  • Ermakov's equation
  • Green function
  • Lewis-Riesenfeld dynamical invariant
  • Propagator
  • Quantum damped oscillators
  • Quantum integrals of motion
  • The time-dependent Schrödinger equation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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