Elastic collision in one of the particles' frame

Homework Statement

A particle B is standing still while another one, A, is moving towards it with initial 4-momentum ##(E,p,0,0)##. Calculate the change in particle A's 4-momentum as viewed from the particle B's rest frame, in terms of the initial energy E and the scattering angle ##\theta##.

The Attempt at a Solution

I am a bit confused about the 4-momentum conservation. Initially we have ##p^i_A=(E,p,0,0)## and ##p^i_B=(m_B,0,0,0)## finally we should have ##p^f_A=(E_f, p_f cos(\theta),p_f sin(\theta),0)## and ##p^f_B=(m_B,0,0,0)##. To get the change in momentum I would do ##p^f_A-p^i_A##. But the total momentum should be conserved in any frame, but I am not sure how does that work here. In order to conserve it, we would need ##E=E_f## and ##\theta=0## but then the problem would be trivial and also physically you can obviously have angles other than 0. What am I doing wrong?

Answers and Replies

mfb
Mentor
Particle B will move after the collision.

maughanster
mfb gave a good answer. After the collision, particle B is not stationary. Maybe this already clear, but the TOTAL momentum is conserved, not necessarily the momentum of each individual particle.