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Let [itex]E_1, E_2, \ldots, E_n[/itex] be [itex]n[/itex] allowed energy levels for a system of electrons. This system can be described by the Fermi-Dirac distribution [itex]f(E)[/itex].

Each of those levels can be occupied by two electrons if they have opposite spins.

Suppose that [itex]E_1, E_2, \ldots, E_n[/itex] are such that

[itex]\displaystyle 2 \sum_{k = 1}^n f(E_k) = 1[/itex]

where the [itex]2[/itex] is due to the degeneracy of states (two electrons allowed for each state). So, can it be stated that in such a system is

*actually*present one electron, that is the result of the sum?

If someone could even explain why, it would be very appreciated.

In any case, thank you for having read.

Emily