Quote by Tarantinism
Actually, if you sum all the probability distributions, for example, the three distributions from those eigenfunctions for l=1, it gives an actual spherically symmetric function.
Your intuition is good, there is no Z axis. Without any external fields, an electron with l=1 would be 1/3 in each orbital, and that's spherically symmetric. When you fix a magnetic field, for example, and you measure number m, then you get the electron in that orbital.

Ok, well the l = 0 orbits are spherically symmetric anyway. So, let's say I have...err, Boron, I think. So I have the 1s and 2s shells are filled, and I have one electron that's spread among the m = 1,0,+1 orbitals, right? But they always taught us that it takes one of the six available places...was that simply misleading?
So when we add more electrons in the l = 1 orbital, they keep spreading themselves among the various available spherical harmonics such that the sum is spherically symmetric?
Thanks for the response!