Thomas-Fermi Atom
Electron density functional theory — precursor to modern DFT (Kohn-Sham)
d²φ/dx² = φ^(3/2) / x^(1/2) — Thomas-Fermi equation (x = r/r_TF, φ(0)=1, φ(∞)→0)
n(r) = (1/3π²)(2μ − 2V(r))^(3/2) — local kinetic energy approximation
r_TF = (9π²/128Z)^(1/3) a₀ ≈ 0.885 Z^(-1/3) a₀ — Thomas-Fermi radius
First DFT (1927): energy as functional of density. Modern DFT (Kohn-Sham 1965) = exact in principle.
Z=18 (Argon) | Total electrons: 18.0