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phos19
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- Fermi energy for arbitrary multiplicity
I ran across the following problem :
Statement:
Consider a gas of fermions and suppose that each energy level has a multiplicity of . What is the Fermi energy and the average energy of this gas when ?
My attempt:
The average occupation number for a state of the th level is:
Usually if the system has a fixed degeneracy, say only the spin degeneracy , one can write the total number of particles as an integral over :
One can than find the Fermi energy in the limit .
But this is not the case when ... Any hints on how to do this ?
Statement:
Consider a gas of
My attempt:
The average occupation number for a state of the
Usually if the system has a fixed degeneracy, say only the spin degeneracy
One can than find the Fermi energy in the limit
But this is not the case when
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