Therefore, the commutator between a translation operator and the position operator is: [ r ^ ^ , T ^ ^ ( x ) ] ≡ ≡ r ^ ^ T ^ ^ ( x ) − − T ^ ^ ( x ) r ^ ^ = x T ^ ^ ( x ) This can also be written (using the above properties) as: ( T ^ ^ ( x ) ) − − 1 r ^ ^ T ^ ^ ( x ) = r ^ ^ + x I ^ ^ where I ^ ^ is the identity operator.