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__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 E

^{i}before the emission and E

^{f}after, so E

^{i}- E

^{f}= ħω. (That I can understand.) ψ

^{i}and ψ

^{f}are eigenvectors of the energy operator H, while E

^{i}and E

^{f}are their corresponding eigenvalues, respectively. He then gives this equation, where A is "any observable":

ψ

^{f}* (AH-HA) ψ

^{i}= ( E

^{i}- E

^{f}) 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?