Fermi-Dirac distribution normalization

[Davide82]

Hi!

I have a little question which is puzzling me.
Maybe it is a very simple question.

It is my understanding that the Fermi-Dirac distribution is a probability density function and, as such, its integral between 0 and infinite should be 1.
When T = 0, the integral gives the chemical potential and so the distribution can be normalized by $$1 / \mu$$.
But if I calculate the integral while T >> 0 I don't understand which could be the normalization factor. Do you have an answer?

Thank you

 

[daveyrocket]

No, the Fermi-Dirac distribution is not a true probability distribution. It tells you the probability of occupation of a state at energy E given the chemical potential, which means that for every energy value the value of f(E) has to range between 0 and 1. It does not get normalized in the way that you're thinking.

 

[Davide82]

Thank you!