I've been thinking about one of the postulates about one particle quantum mechanics, it says that whenever we measure an energy value, we get one of those eigenvalues. Firstly, pretty much 99% of the stuffs I know in nonrelativistic QM applies in the realm of electromagnetism. I just don't think a particle stuck in a classical gravity well is realistic. (I may be wrong). So in QED what do we mean by measuring energy? I believe in all the experiments, we measure the photons emitted by states transitions and use that as the energies. I feel fundamentally, the reason why these photon energies are discrete have to do with QED. The question is, how then? is it possible to deduce this postulate from first principles in QFT? I know it is difficult to treat bound states in QED (specially in a perturbation sense...when interactions aren't small at all). So perhaps there are some simple intuitive explanations?