Let a particle of charge e and rest mass m, initially at rest in the laboratory, scatter a photon of initial frequency v_i. this is called compton scattering. suppose the scattered photon comes off at an angle theta from the incident direction. use conservation of four-momentum to deduce that the photon's final frequency v_f is given by 1/v_f = 1/v_i + h (1-cos theta/m)
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