The hypothesis which the Compton Scattering experiment most clearly
highlights is the idea that individual photons from light of frequency
should carry a momentum 
, where h is Planck's
constant, 
. This hypothesis arises
naturally as a consequence of the correspondence principle and the
observation that, as a direct consequence of Maxwell's equations,
a classical electromagnetic wave of energy U carries a momentum
.
We can thus perform a thought-experiment where a monochromatic beam of
light of frequency 
and energy U is directed at an absorbing
plate. With our faith in Maxwell's equations, we know that after the
plate absorbs the radiation, it will recoil in the experiment with a
momentum given by 
. On the other hand, from the Planck
Radiation formula and the photoelectric effect, we know that
microscopically the energy of the beam arrived at the plate in a
series of 
discrete packets or photons. To explain
the recoil of the plate from this microscopic picture, it is natural
to associate with each of the photons a momentum as well as an energy.
To explain the magnitude of the observed recoil, the average momentum
carried by the photons of must be the total recoil momentum divided by
the number of photons, 
. Since all
photons of frequency 
carry precisely the same energy, a further
natural working hypothesis would be that they all carry the same
momentum as well so that 
. Note that this cannot be
concluded strictly from the though experiment, however, as we shall
see this hypothesis is completely consistent with the experimental
observations.