## Abstract

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 language | English |
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Pages (from-to) | 4173-4180 |

Number of pages | 8 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 39 |

Issue number | 16 |

DOIs | |

State | Published - 21 Apr 2006 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy