I am having hard times, trying to find out how the FermiDirac and BoseEinstein distributions give you at a limit the Boltzmann's one.(adsbygoogle = window.adsbygoogle || []).push({});

Let's see the FermiDirac one:

<n_{i}>= 1/ { 1+ e^{[β(εi-μ)] }}

where β=1/kT, where T:Temperature and k the Boltzmann's constant.

As we know the limits from quantum to classical physics for these are either at high Temperatures (so T→∞ So β→0) or low densities (n<<n_{Q}=(2πmkT/h^{2})^{3/2}).

So I am trying to put on Fermi-Dirac's distribution the limit β→0.

I just want you to reconfirm my work:

I multiplied on numerator and denominator with e^{[-β(εi-μ)] }

getting:

e^{[-β(εi-μ)] }/ (e^{[-β(εi-μ)] }+1)

Now again for β→0 I get

e^{[-β(εi-μ)] }/2

which is half what I want to get....

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# FermiDirac-BoseEinstein-Boltzman derivation

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