Q:

An ideal gas of fermions, with mass m and Fermi energy xT , is at rest at zero temperature

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An ideal gas of fermions, with mass m and Fermi energy εF , is at rest at zero temperature. Find expressions for the expected values vx and vx2, where v  is the velocity of a fermion.

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At zero temperature, the expected value of the (single-particle) energy is calculated in terms of the density of states D (ε). With D (ε) = Cε1/2, we have

Note that

 

in contrast to the predictions of the classical equipartition the- orem.

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