Orbital |n, l, m⟩
Orbital info
Energy: — eV
⟨r⟩: — a₀
State: —
Color = |ψ|²
Green=high, Black=zero
Constraints: |m|≤l, l<n
Green=high, Black=zero
Constraints: |m|≤l, l<n
DFT replaces the many-body wavefunction with the electron density n(r). For hydrogen, exact solutions ψ_nlm(r,θ,φ) are known. The Kohn–Sham equation −½∇²ψ + v_eff[n]ψ = εψ maps to non-interacting electrons in an effective potential v_eff = v_ext + v_H + v_xc.