Friedel Oscillations: Screened Charge Density Around an Impurity

A point charge dropped into a metal is not screened smoothly — the sharp Fermi surface of the conduction electrons forces the induced charge density into a ringing, slowly-decaying oscillation known as a Friedel oscillation. This simulator renders that screening cloud as a real 3D field of instanced points around a central impurity, sized and colored by the sign and magnitude of the local electron density perturbation δn(r), with a live probe shell you can drag to any radius. A one-click comparison against the cruder Thomas–Fermi approximation — which predicts smooth exponential decay instead — makes the difference between the two screening pictures immediately visible, alongside live readouts of the oscillation wavelength and the Thomas–Fermi screening length, both of which are set entirely by the Fermi wavevector k_F.