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The Ground State of a Fermi Gas

# The Ground State of a Fermi Gas - electrons in a metal...

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The Ground State of a Fermi Gas We can solve for the Fermi energy by setting the total number of particles below that energy equal to the total number of particles in the system. We obtain: = (3 Π 2 n ) 2/3 We use the term "ground state" to refer to the state in which no fermions are excited to higher energy states beyond the Fermi energy. We can calculate the energy of the ground state by summing up the energies of the orbitals below the Fermi energy, to obtain: U gs = N We can go through and calculate all of the other relevant quantities just as we did for the ideal gas. The Fermi gas appears throughout any study of physics. Electrons form a Fermi gas. The
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Unformatted text preview: electrons in a metal, the "sea of electrons", act as a Fermi gas. In astrophysics, white dwarf stars are prevented from collapsing upon themselves by the pressure of the Fermi gas and the resistance it gives to having its orbitals pushed together. Bose Gas A Bose gas is a gas consisting of bosons. We will treat the topic briefly as above with the Fermi gas. Bose-Einstein Distribution Function An orbital can support any number of bosons, which fundamentally changes the Gibbs Sum and thus the distribution function. Instead of summing over N = 0, 1 we must sum over all N . The final result is: f ( ) =...
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