#  Thomas-Fermi model: universal eqn, form of potential, comparison with observations.
Showed a plot of the single particle energy levels of the Thomas-Fermi-Dirac potential
(Fig. 13.8 from Schwabl, which is taken from R. Latter, Phys. Rev. 99, 510 (1955)
which revealed an order of filling and approximate degeneracy of shells that is in fact
quite close to what is seen in atoms. [Thomas-Fermi-Dirac is an improvement of Thomas-Fermi
taking into account exchange energy.]

# Density functional theory: introduced by Kohn and Hohnberg in early '60's, just won Nobel
prize. It is an "exactification" of the Thomas-Fermi approach. Amazingly, one can formulate
the problem of N electrons in an arbitrary external potential exactly (in principle) in terms
of just the electron density n(r). The idea is explained on the page of Kohn's Nobel lecture
that was handed out in class (Rev. Mod. Phys., Jan. 2000).

# The Thomas-Fermi approximation to the kinetic energy term as that of a degenerate
local Fermi gas is the weakest point. Kohn and Sham improved on this with a kind
of hybrid of Thomas-Fermi and Hartree approaches, using a simple product of orbitals in
the Thomas-Fermi potential to compute the kinetic energy functional. One can then
look for a self-consistent solution by iteration.

# The universal functional appearing in the density functional approach can be
approximated by successively more accurate expressions.

Midterm exam.