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As far as I know, in the old quantum theory, a system can only reside in a stationary state. There was no Hilbert space, and no linear superposition. Or, a system cannot be simultaneously in two stationary states.

So, what is the first experimental observation showing that a system can be in a non-stationary state (or a generic state)?

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    $\begingroup$ Coherence emerged as a side effect of reconciling classical electrodynamics with early quantum theory, not as a result of experimental observations. Observations that "exhibit" coherence were known long before that (wave optics), but viewed differently. See Who was first to detect photons in the double slit experiment? A cruder earlier version of "superpositions" was de Broglie's pilot wave theory $\endgroup$
    – Conifold
    Commented Nov 21, 2016 at 1:07
  • $\begingroup$ If you have in mind coherent states like coherent light waves, then you can't really talk about that as quantum coherence in the context of the old quantum theory. Bohr et al. wanted to quantize the atom while keeping the electromagnetic field classical. $\endgroup$
    – user466
    Commented Nov 23, 2016 at 5:35

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