Main Question or Discussion Point
When calculating eigenstates in the hydrogen atom one finds plenty of eigenstates with angular dependence. The s orbitals are spherically symmetric, but an orbital like 2p is not, there is some angular dependence through the spherical harmonics. But why is there angular dependence? It is a totally spherically symmetric problem so how can there be? Certainly, starting from the nucleus and going out in one direction should not be any different from going out in any other direction. How is the angular dependence to be interpreted?