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In a 3D oscillator, the energy levels are known to be $(n_x + n_y + n_z + \frac{3}{2})\hbar \omega = (n + \frac{3}{2})\hbar \omega$.

Say for $n = 1$, any of the $n$'s can be $1$ and the rest are $0$. For $n = 2$ and $3$, same concept applies.

How do I use this information about degeneracy to suggest values of $\ell$ in spherical harmonics $Y_\ell^m$?

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