For a translationally invariant system in one dimension with the Hamiltonian that satisfies f(x+a)= R(x), where a is a constant displacement Does the translation operator, given by T(x) = (x + a), commute with the Hamiltonian? Show either way. Note that the translation operator is a unitary operator.

For a translationally invariant system in one dimension with the Hamiltonian that satisfies f(x+a)= R(x), where a is a constant displacement Does the translation operator, given by T(x) = (x + a), commute with the Hamiltonian? Show either way. Note that the translation operator is a unitary operator.