Time reversal for modified oscillators

R. Cordero-Soto, Sergei Suslov

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We consider a new completely integrable case of the time-dependent Schrödinger equation in ℝn with variable coefficients for a modified oscillator that is dual (with respect to time reversal) to a model of the quantum oscillator. We find a second pair of dual Hamiltonians in the momentum representation. The examples considered show that in mathematical physics and quantum mechanics, a change in the time direction may require a total change of the system dynamics to return the system to its original quantum state. We obtain particular solutions of the corresponding nonlinear Schrödinger equations. We also consider a Hamiltonian structure of the classical integrable problem and its quantization.

Original languageEnglish (US)
Pages (from-to)286-316
Number of pages31
JournalTheoretical and Mathematical Physics
Issue number3
StatePublished - 2010


  • Cauchy initial value problem
  • Green's function
  • Hyperspherical harmonic
  • Nonlinear Schrödinger equation
  • Propagator
  • Schrödinger equation with variable coefficients
  • Time reversal

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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