GROUP THEORY AND HARMONIC OSCILLATORS IN THE PLANE Page No: 2581-2588

Gabriel Y. H. Avossevou

Keywords: Harmonic oscillators, Dynamical symmetry group, Spectrum, Degeneracy.

Abstract: We show explicitly in this contribution that with a correct identification of the underlying symmetry group to the physical system that represent a finitely many harmonic oscillators in the Euclidian plane, namely the dynamical symmetry group U(rd)=UN(1)×SU(rd), it’s possible to remove fully the degeneracy that such systems carry for which, furthermore, there is no need to show the importance in physics. In this group notation, r=2 refers to as the dimension of the plane, while d is the number of particles.



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