Relativistic particles in a gravitational field
Consider N relativistic ideal-gas particles at temperature T. The particles are confined to a three-dimensional box of area A and 0
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1. Find the probability distribution for the height of a single particle, i.e.: P(z1).
2. Find the average height of a single particle.
3. In what way did your answer for the average height depend on the relativistic nature of the particles?
4. Find the probability distribution for the energy of a single particle, E1 = |p1|c + mgz1, including the normalization constant.