Past exam of the physics A course of the University of Cambridge / 2014 / Paper 2 / Section A / 4

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- Solution 4

Solution

The mean energy of a two-dimensional Fermi gas follows from its constant density of states

g

for nonrelativistic quadratic dispersion. At zero temperature, states below

ϵ_{F}

are filled, so

N = g ϵ_{F}, U = \int_{0}^{ϵ_{F}} g ϵ d ϵ = \frac{1}{2} g ϵ_{F}^{2}, \frac{U}{N} = \frac{ϵ _{F}}{2} .

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