Why does an(adsbygoogle = window.adsbygoogle || []).push({}); atomemit discrete frequencies of light?

Solving the Schrodinger wave function for the hydrogen atom (that is a single particle representing an electron bound by a spherical potential) we find that it has discrete energy levels. Plotting every possible value of [itex]f[/itex] in [itex]E'-E = \hbar f[/itex] where [itex]E'[/itex] and [itex]E[/itex] are the different energy levels of eigenstates we recover the emission spectra.

What I don't understand is why we only see these discrete energy levels. According to the superposition principle, the wave function could be in a superposition with expected energy [itex]\tfrac{1}{2}(E'+E)[/itex] but differences from these levels don't show up on the emission spectra. The measurement postulate seems relevant, "measurement" collapses a wave function into an eigenstate, this seems to be happening before and after the photon emission, can anyone explain why?

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# Why does a photon emit discrete frequencies of light?

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