Suppose | r ⟩ ⟩ is an eigenvector of the position operator r ^ ^ with eigenvalue r . We have T ^ ^ ( x ) r ^ ^ | r ⟩ ⟩ = T ^ ^ ( x ) r | r ⟩ ⟩ = r | x + r ⟩ ⟩ while r ^ ^ T ^ ^ ( x ) | r ⟩ ⟩ = r ^ ^ | x + r ⟩ ⟩ = ( x + r ) | x + r ⟩ ⟩