The variance σX^2=⟨(X^−⟨X^⟩)^2⟩ of an operator, X^, is a measure of how large a range its possible values are spread over (the standard deviation is given by σ=sqrt(σ2)). Suppose that |X⟩ is an eigenstate of some operator X^, what is the variance of X^ in this state? You may assume that |X⟩ is normalized (⟨X|X⟩=1).

Question

Note that the expectation value of an operator in the state |ψ⟩ is given by ⟨O^⟩≡⟨ψ|O^|ψ⟩.