Consider a collision between a photon with frequency 
moving
in the x direction, with an electron of rest mass 
initially
at rest [ see Figure 2.3 ].
Figure 2.3: Diagram illustrating Compton scattering.
Before the collision, the four- momenta of the photon and electron are
After the collision we have
where 
is the photon's frequency after the collision, v is the
speed of the electron and 
, 
are shown in Figure 2.3.
Conservation of four- momentum gives
Rearranging and squaring we get
Using 
and 
we obtain
which gives the Compton scattering formula
