 Solution

ID: past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2014/paper-2/section-a/4/solution

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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