If a translation operator T ^ ^ ( x ) acts on the state | ψ ψ ⟩ ⟩ , creating a new state | ψ ψ 2 ⟩ ⟩ then the expectation value of position for | ψ ψ 2 ⟩ ⟩ is equal to the expectation value of position for | ψ ψ ⟩ ⟩ plus the vector x . This result is consistent with what you would expect from an operation that shifts the particle by that amount.