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•• Consider a three-level quantum system, with non-degenerate energy levels 0ε, +, and +2ε. (A physical example of such a system is a spin S = 1 magnetic moment in a magnetic field.) (a) Write down the partition function Z for this system. (b) Write down the expression for the thermal average energy 〈E〉 of this system. (c) Show that in the low-temperature limit kT ≪ ε, the energy and specific heat of this system are identical to those of a two-level system. (d) Show that in the high-temperature limit kT ≫ ε, the heat capacity of this system, like that of a two-level system, approaches zero.
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