(a) Explain the important difference between classical and quantum particles. Discuss the requirements that determine whether a particle obeys Bose-Einstein or Fermi-Dirac statistics.
(b) Under what conditions is it possible to expect a transition from Fermi-Dirac to Maxwell-Boltzmann statistics? Is it correct to say that the Boltzmann Distribution is the limiting case of the Fermi-Dirac Distribution?
(c) Assume that in a hypothetical system there are only three particle states, with energies e1, e2 and e3. Determine the maximum number of fermions in this system.
(d) Show that the entropy of an ideal fermion gas is in agreement with the Third Law of Thermodynamics.