Thomas-Fermi Atom — Density Functional Theory

Semiclassical electron density from ODE shooting method

Atomic number Z26 (Fe)

Grid points500

x_max15

Z: 26

N_e (integrated): —

φ'(0): —

r_TF: —

Thomas-Fermi ODE: φ'' = φ^(3/2)/√x. Boundary conditions: φ(0)=1, φ(∞)=0. Electron density: n(r) = Z/r · (Z^(1/3)·φ(r)/a₀)^(3/2) × (1/3π²)(2me/ℏ²)^(3/2). Solved by shooting.