Evaluate the commutator of the Hamiltonian H = V ( { X i } ) + ∑ ∑ n P n 2 2 m with the position operator X n and the momentum operator P n = − − i ℏ ℏ d d X n of particle n, [ H , X n P n ] = X n [ H , P n ] + [ H , X n ] P n = i ℏ ℏ X n d V d X n − − i ℏ ℏ P n 2 m .