I was thinking back to my QM class last semester. My teacher derived what the orbitals of the hydrogen atom should look like. I just realized something a little strange about the result that it did not occur to me at the time to ask: How is it that orbitals resulted from a spherically symetric problem which were not themselves sherically symetric? Unfortunately I can not find the whole derivation, but from what I remember, lobes appeared that were either aligned with, or perpendicular to, the polar axis that was used for spherical coordinates. Since the choice of this axis was arbitrary, how did it end up affecting the result? Or maybe it didn't and I'm missing something, or remembering something incorrectly?