A little behind in this subject, but I understand raising & lowering operators to almost be factors of the Hamiltonian operator. raising - Ahat dagger = 1/√2 (x/a - a*(δ/δx)) lowering - Ahat = 1/√2 (x/a + a*(δ/δx)) I also have the Hamiltonian as; Hhat = (Ahat dagger * Ahat + 1/2) hbar ω0 Is this an identity defining the Hamiltonian? Help! A little pointer in the right direction or an explanation to provide a bit of clarity would be great. Thank you.