Journal of Mathematical Physics

The symmetry group of the harmonic oscillator and its reduction

Toshihiro Iwai

Published Jun 1, 1982• 14 citations

Abstract

The symmetry of the harmonic oscillator is dealt with in the Hamiltonian formalism. Unitary operators representing the symmetry are studied from this point of view. Of additional interest is reduction of the symmetry group SU(4) for the four-dimensional harmonic oscillator. Subspaces are determined from the representation spaces for SU(4) so as to give those for SO(4).

DOI: 10.1063/1.525472

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