commutator practise chemical Engineering

Evaluate the commutator (Pz, (P2, H]] where pz is the x-component of the momentum operator and H Hamiltonian of the system. p +V() is the 2m Use this result to prove the following sum rule: 12 (En Em)|(n|pz|m)|? ( (m? m a2V az2 m 2 n where (n) and (m) are eigenvectors of H with eigenvalues En and Em, respectively