When is an atomic electron's probability density spherically symmetric?

[CollectiveRocker]

I realize that electron probability density is the probability of finding an electron in a given volume, but as I was working on some homework, I wasn't sure how this fact would apply. Under what circumstances is an atomic electron's probability-density distribution spherically symmetric?

 

[Dr Transport]

When the wave function's angular quantum number is 0 the probaility density will not depend on any angular coordinates.

 

[CollectiveRocker]

Thank you. Why exactly does this work?