An electron moving to the left at 0.8c collides with an incoming photon moving to the right. After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon?
This problem can actually be solved most easily in the elementary way, i.e. by simply writing down conservation of energy and momentum and solving these equations. So, perhaps you need to study some other problems, I'll suggest a few after finishing this problem.
Let's introduce the following four-vectors:
P1 = four-momentum of electron before collision
P2 = four-momentum of electron after collision
Pf1 = four-momentum of photon before collision
Pf2 = four-momentum of photon after collision
Then we have:
P1 + Pf1 = P2 + Pf2 (1)
Let's first solve this equation without using four-vector algebra. We just rewrite it as:
P1 - P2 = Pf2 - Pf1 (2)
In c = 1 units we have:
P1 = (m gamma1, -m gamma1 v1)
P2 = (m gamma2, m gamma2 v2)
Pf1 = (E1, E1)
Pf2 = (E2, -E2)
where v1 = 0.8 and v2 = 0.6 are the ...
A detailed solution is given.