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I am not sure why you believe that a single
photon must be monochromatic. It is true that the
often formalism deals with it that way.
If there
is just a single frequency associated with a
photon, how long must it be? From the Fourier
analysis I think you get infinite. If there is no
uncertainty in the energy, what is the uncertainty
in when the photon was somewhere. Again infinite.
( These two questions are related.)
One can experimentally measure the length of a
single photon.
Use an interferometer, such as a
Michelson, and a light source that emits a single
transition (use filters or gratings as needed),
and that emits at a single photon rate. The
interference pattern falls apart if the difference
of the two optical paths lengths exceeds the
length of a photon because it can no longer
interfere with itself. Thus photons have a finite
length and the photons are not truly
monochromatic.
We, physicists, almost always work in systems of
energy eigenstates, but it is not required.
A single isolated, at rest, atom emits a photon with
a energy spread associated with the natural line
width of the transition.