Non spherical solutions of a spherical potential well?

[nista]

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?
Thanks in advance for your comments

Roberto

 

[Meir Achuz]

If there is no preferred direction, so all the m values for each L are equally likely, the full probability distribution will be spherically symmetric. If there is a defined z axis for which different m values have different amplitudes, there will be an angular distribution.