Symmetry of boundary conditions cashes out in symmetry of solutions in two ways. The obvious one is solutions that are themselves symmetrical. The less-obviou

Symmetry of boundary conditions cashes out in symmetry of solutions in two ways. The obvious one is solutions that are themselves symmetrical. The less-obvious one is families of solutions, where the symmetry maps one solution to another. All of the "s" states are spherically symmetric. The "p" (and higher) states aren't spherically symmetric, but are instead a basis for an entire family of states that are related to each other through rotations.