Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

I've search for my question and found no answer. I think it should be pretty simple...

Fermi energy corresponds to the last occupied energy, as I understand it. So, energy levels in the Fermi gas are all filled with two electron of opposite spins, up to the Fermi energy. Saying it that way, one could conclude that at zero Kelvin,there is a probability of 1 of finding all the electrons in energy levels equal or below the Fermi energy.

But, and this puzzle me, the probability of finding an electron at the Fermi level is one half. To see this, take the Fermi-Dirac statistics and put E = Ef which gives one half. So, at zero Kelvin (or other temperatures...),the probability of finding all the electrons in energy levels lower or equal to Fermi energy is one half. This is in contradiction with what i've said in the first paragraph.

Could someone explain me what is the matter about this one half? I don't understand its physical origin, and I don't see at what energy(ies) the other one half of the time the electron are supposed to be...

Thanks in advance,

TP

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# Fermi-Dirac statistics at the Fermi level

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