Show for a single orbital of a fermion system that = (1 ), If is the

Question:

Show for a single orbital of a fermion system that

<(∆N)2> = (1 – ),

If is the average number of fermions in that orbital. Notice that the fluctuation vanishes for orbitals with energies deep enough below. The Fermi energy so that = 1. By definition, ∆N ≡ N –