Consider a degenerate Fermi gas of non-interacting, non-relativisitic, particles in two dimensions (this might be
a model for electrons in a thin metallic film).
a) Find the density of states g(€).
b) Find the Fermi energy and the T=0 energy density.
c) Using the the fact that the particle density n is given by
n = de eB(E-H)+1 g(£)
find the chemical potential as a function of temperature, (T), for fixed density n, by doing this integral exactly.
You may have to look up an integral in an integral handbook! Using the exact expression for (T), find a
simpler approximation that holds at low T<found in three dimensions with the Sommerfeld expansion?
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