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Sep 13, 2020 at 8:38 comment added Superfast Jellyfish I would like to add a comment to this already excellent answer, now that I have studied this a bit. The harmonic evolution in time of the fields come directly from the fact that energy goes as $\sim n\hbar\omega$. That means that the time evolution of the state goes as $e^{-in\omega t}$. The reason these phases don’t cancel out during expectation of fields because the energy eigenstates are not field eigenstates. In fact the phase factors of the field’s expectation value works out to be exactly $e^{-i\omega t}$
Jan 15, 2020 at 14:49 vote accept Superfast Jellyfish
Jan 15, 2020 at 14:39 history answered user245141 CC BY-SA 4.0