PHYS 317 - Reading Assignment #23

  1. In equation (7.42), why is the total energy less than N*epsilonF?

    N is the number of particles in the system. As they fill up the available states from lowest energy upwards, they take energies from 0 to epsilonF. Therefore the average energy per particle must be less than epsilonF.

  2. In going from a T=0 fermion gas to a T>0 fermion gas, is it accurate to say that each fermion gains an energy of roughly kT?

    Absolutely not. Only a fermions within an energy of kT of the Fermi energy can possibly go to an excited with a thermal energy of kT. This is a often tiny fraction of the actual fermions.

  3. What is the physical origin of degeneracy pressure?

    Basically the Pauli exclusion principle. It forces an ideal electron gas to contain highly energetic electrons, and these provide a significant pressure even at absolute zero.

  4. Give a definition for the density of states g(epsilon) in words. Hint: look around equation (7.50), not later.

    The number of single-particle states per unit energy. So integrating over energy give the number of single-particle states.
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