This proof has an issue related to the domains of the operators involved. For the proof to make sense, the vector B ^ ^ | Ψ Ψ ⟩ ⟩ has to be in the domain of the unbounded operator A ^ ^ , which is not always the case. In fact, the Robertson uncertainty relation is false if A ^ ^ is an angle variable and B ^ ^ is the derivative with respect to this variable. In this example, the commutator is a nonzero constant—just as in the Heisenberg uncertainty relation—and yet there are states where the product of the uncertainties is zero. (See the counterexample section below.) This issue can be overcome by using a variational method for the proof, or by working with an exponentiated version of the canonical commutation relations.