I'm in chapter two of H. S. Green's Matrix Mechanics and at a sticking point. In section 2.2 he gives the following scenario: An atom emits a photon with angular velocity ω, it has energy Ei before the emission and Ef after, so Ei - Ef = ħω. (That I can understand.) ψi and ψf are eigenvectors of the energy operator H, while Ei and Ef are their corresponding eigenvalues, respectively. He then gives this equation, where A is "any observable": ψf * (AH-HA) ψi = ( Ei - Ef ) ψ f * A ψ i. Although he briefly mentions commutation a couple paragraphs before this point, it's not enough to explain where this relationship comes from. Can anyone help me out?