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:(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# The significance of commutation

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