The Fermi-Dirac gas

In this lecture I discuss the Fermi-Dirac gas. I begin by expressing important thermodynamic quantities as integrals using the concept of density of states. I then develop the theory of Fermi-Dirac integrals and show how they are equivalent to the polylogarithm function. Finally, I use these functions to derive closed form expressions for the number of particles, pressure and internal energy, allowing me to write down the equation of state for the Fermi-Dirac gas.

[@JaGWiREE]

If you upload future videos it would be useful to do small edits where mistakes are made as you did in a prior video for a missing prefactor. I wasted a few minutes working out the calculations myself several times and error-checking urs, but a few minutes later in the video you do so anyway so it was a bit of a waste of my time feeling crazy I had made an error. I've gone through this content several times over the last 5 years and I've gotten tripped out and seen others tripped up in these integrals including Kardar himself so I think it is quite common for us to make these slight housekeeping errors when manipulating these more tricky integrals.