Two particles collide, COM frame, relativistic velocities.

[EdgyWaters]

Homework Statement

2-body, COM frame collision
a+b ---> c+d
E = Ea+Eb = Ec+Ed
Show that
dE/dPf = Vc+Vd
Show that the answer is the same when the velocities are relativistic
I don''t know how to work out the relativistic aspect of the question.

Homework Equations

The Attempt at a Solution

E = Pc^2/2Mc - Pd^2/2Md
(Pf^2)/2(I/Mc + I/Md) = (Pf^2)/2(Md+Mc/McMd)
dE/dPf = Pf(1/Mc+I/Md) = Vc + Vd

 

[mfb]

What is Pf?
How can E depend on anything if it is fully determined by the initial (or final) state?

If you can solve it in the Newtonian case, replace all Newtonian equations with their relativistic versions, and see if it still works.