In Quantum Mechanics and in semiconductor materials, the number of electrons N in conduction band is usually computed as follows:
N=∫+∞Ecgc(E)f(E)dE
where gc(E) is the density of states of electrons with respect to energy and f(E) is the Fermi-Dirac distribution.
When the density of states is computed, it is taken into account that each energy level can have two electrons with opposite spins: even if the level is single, the electrons may be two.
f(E) is always said to be «the probability that an electron actually occupies a state with energy level E»: but what if the state is a "double" state? Is this probability halved of doubled? In other words: which is the approach followed to obtain the above integral?
This is mentioned in Wikipedia, but without a proof. The cited source is too wide to be used.
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