Tensors and Relativity: Chapter 2
Example 2.2
Next: Index Up: Relativistic dynamics Previous: Example 2.1
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