Why does an atom emit 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 f in E'-E = \hbar f where E' and E 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 \tfrac{1}{2}(E'+E) 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?