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Is it because all levels upto fermi level are filled or all degeneracies of the energy levels that are present occupied at T = 0k .

In deriving the average occupation no. for a deg fermi gas , we have used classical idea of momentum that is integrating over a sphere of p^2 dp , why not qntm mechanical operator form since this a quantum gas.

Also in calculating average N we have an integral of (E)^1/2 dE within limit 0 to Ef where Ef is fermi energy level , now while evaluating this we don't consider the E= 0 state i.e ground state because if we put 0 then avg N = 0 , what's the thought behind this ?

I had posted this in general section , got no reply , atleast someone reply here