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Two one-dimensional relativistic particles
Consider two one-dimensional relativistic ideal-gas particles with masses confined to a one-dimensional box of length L. Because they are relativistic, their energies are given by EA = |pA|c and EA = |pB|c. Assume that the particles are in thermal equilibrium with each other, and that the total kinetic energy is E = EA + EB. Use the usual assumption that the probability density is uniform in phase space, subject to the constraints. Calculate the probability distribution P(EA) for the energy of one of the particles.
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