I applied the [spherical harmonic equation](http://mathworld.wolfram.com/SphericalHarmonic.html) on the `SphericalHarmonicY` functions like this:

```
Simplify[(1/Sin[θ]) D[Sin[θ] D[SphericalHarmonicY[l, m, θ, ϕ], θ], θ] + 
    (1/Sin[θ]^2) D[SphericalHarmonicY[l, m, θ, ϕ], {ϕ, 2}]]

```

And it returns a sum of factors with $Y^{m}\_{l}(\theta, \phi)$, $Y^{m+1}\_{l}(\theta, \phi)$ and $Y^{m+2}\_{l}(\theta, \phi)$

This is counterintuitive. I thought these were the eigenfunctions of the operator. I feel like I might be missing something basic here.