For electrons with an energy >> mc2, where m is the rest mass of the election,
Question:
(a) Show that in this extreme relativistic limit the Fermi energy of a gas of N electrons is given by
εF = hπc(3n/π)1/3,
where n = N/V.
(b) Show that the total energy of the ground stale of the gas is
U0 = ¾ NεF.
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