I am having trouble understanding the subtleties of this topic, which we've just covered in my QM course. I guess, if I understand correctly, that the superposition of eigenstates is not necessary an eigenstate itself, unless the states are degenerate. I'm not sure if I really understand why this is (unless this is one of those things that "just is" in quantum and I'm not supposed to get it). Yet it seems (also from my course discussions) that the superposition of solutions to the Schrodinger equation is also a solution, regardless to things being degenerate, or what not. And I am not sure if I understand how this relates to the commutator relations - if two operators commute, they share some eigenstate, right? How does it relate to the superposition and degeneracy? If anyone can elucidate this subject I'd be all sorts of grateful!