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Homework Statement
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.
Homework Equations
Given, we have the initial and final four-vectors of the photon and electron:
P_{photon,i} = (E_{i}, E_{i} n_{i})
P_{photon,f} = (E_{f}, E_{f} n_{f})
P_{electron,i} = (m_{e}, 0)
P_{electron,f} = (gamma m_{e}, gamma m_{e}v_{i})
The Attempt at a Solution
Using conservation of momentum, we get this expression:
P_{photon,i} + P_{electron,i} = P_{photon,f} + P_{electron,f}
This is where I get confused. Our tutor solved for the final electron term and then squared both sides like so:
|P_{electron,i}|^{2} = |P_{photon,f} + P_{electron,f} - P_{photon,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?