Quantum Billiard Stadium — Wave Function Scarring

Bunimovich stadium: classically chaotic billiard. Quantum eigenstates scar along unstable periodic orbits.

|ψ|² density (finite-difference eigenstate)

Classical ray trajectory

Eigenstate # 15

Stadium width a 0.50

Color map

Level n: 15

Eigenvalue ≈ —

Scar index: —

Heller (1984): quantum eigenstates concentrate along unstable classical periodic orbits — "scars". Predicted by semiclassical theory, confirmed numerically and experimentally in microwave billiards. The stadium billiard (Bunimovich 1979) is the canonical chaotic system.