Hey all, this is my first post to the forum, but I've been reading for years. Anyways, I was reviewing a solution to a Compton Scattering derivation we learned in class, and am still trying to make sense out of it.
Given, we have the initial and final four-vectors of the photon and electron:
Pphoton,i = (Ei, Ei ni)
Pphoton,f = (Ef, Ef nf)
Pelectron,i = (me, 0)
Pelectron,f = (gamma me, gamma mevi)
The Attempt at a Solution
Using conservation of momentum, we get this expression:
Pphoton,i + Pelectron,i = Pphoton,f + Pelectron,f
This is where I get confused. Our tutor solved for the final electron term and then squared both sides like so:
|Pelectron,i|2 = |Pphoton,f + Pelectron,f - Pphoton,i|2
Is this action legal? Don't you have to square them first, then solve for the final electron term? Please, someone help clarify this. Everyone I ask seems to not even think twice about it. Is it really just a trivial step?