An ideal Fermi gas under uniform gravity

We consider an ideal Fermi gas in a container subject to a uniform gravitational field at absolute zero temperature. Under a semiclassical approximation, we examine the density profile of the particles and derive an expression for the chemical potential. A critical value of the chemical potential separates the weak- and strong-gravity regimes, and the kinetic and potential energies of the Fermi gas are determined in both regimes.