The 3-dimensional harmonic oscillator has SU(3) symmetry. This is stated in many papers. It seems to be due to the spherical symmetry of the system. (After all, the idea of a 3d harmonic oscillator is that a mass is attached to the origin with a spring, and that the mass can move in 3 dimensions, with no gravity involved.)(adsbygoogle = window.adsbygoogle || []).push({});

But I have an issue. If this system has SU(3) symmetry, the 8 generators of SU(3) must somehow act on the various eigenstates. How exactly does this happen? Is there a book or a paper on this?

For example, the eight Gell-Mann generators of SU(3) must transform the states of the harmonic oscillator. What do they do? Do they rotate the state? How? Why are there 8 of them?

Thank you for any advice in this matter.

Cheers

François

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# 3-d harmonic oscillator and SU(3) - how to imagine it?

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