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Eq. (15.29) is the distribution of single-particle energies in a three-dimensional ideal gas. Derive the corresponding expression for the case of a two-dimensional ideal gas. [Hint: Instead of considering a shell of states in 3-D k space, consider a ring of states in 2-D k space.] (A physical example of a 2-D gas is the electron gas that forms at the interface between doped GaAs layers in some semiconductor devices.)
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