Noncommuting contractions of oscillators with constant force

Jamil Daboul, Kurt Bernardo Wolf

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We find two noncommuting contractions of the Lie algebras and , realized as the symmetry algebras of N-dimensional isotropic harmonic and repulsive oscillators of spring constant k ∈ ℜ, with a constant force of magnitude f. The contraction limit to the symmetry algebra of the N-dimensional free system is (k, f) → (0, 0). We take two paths in this plane, determined by the order of contraction of the two parameters, and show that they yield two closely related - but distinct - Euclidean-type symmetry algebras for the common contracted system. We also show briefly how the wavefunctions of the one-dimensional harmonic oscillator reduce to plane waves along the above two paths.

Original languageEnglish
Pages (from-to)4173-4180
Number of pages8
JournalJournal of Physics A: Mathematical and General
Issue number16
StatePublished - 21 Apr 2006

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy (all)


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