## Non spherical solutions of a spherical potential well?

Hi all
just a question about the understanding of the solutions of a spherical potential well.
What is the physical sense of solutions which have no spherical symmetry?
I just would think that the probability of finding a particle
whose state is described by one of the eigenstate of the Hamiltonian should not depend on the angular coordinate as the
problem as spherical symmetry. However for solutions with angular momentum larger than 0 this not the case. Why?