Degeneracy of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Dimensional, Isotropic, Harmonic Oscillator

Abstract

We show that what has previously been considered the "accidental" degeneracy in the energy levels of the $n$-dimensional, isotropic, harmonic oscillator is actually a consequence of its symmetry group. The additional symmetry, beyond the $n$-dimensional rotation group, arises from the symmetry between the coordinates and momenta.