### D.64 Angular momentum uncertainty

Suppose that an eigenstate, call it , of is also an eigenstate of . Then must be zero, and the commutator relations say that this is equivalent to 0, which makes also an eigenvector of , and with the eigenvalue zero to boot. So the angular momentum in the -​direction must be zero. Repeating the same argument using the and commutator pairs shows that the angular momentum in the other two directions is zero too. So there is no angular momentum at all, is an state.