My teacher said that angular momentum doesn't have orientation in space - but how can that be? Isn't cos(theta) = L_z / |L vector| ? Also (an unrelated question) could somebody give an example of how the integration process goes when you are trying to get an expectation value for something which isn't an eigenfunction? i.e. I know if it's an eigenfunction, everything normalizes so you just get the observable as the expectation value. But what if it isn't?