The Bunimovich stadium — two semicircles joined by straight segments — is a paradigmatic fully chaotic billiard. Classical trajectories are ergodic and mixing.
Quantum eigenstates (−ℏ²/2m ∇²ψ = Eψ inside, ψ|∂Ω=0) show quantum chaos signatures: irregular nodal lines, Berry's random wave conjecture (eigenfunctions look like superpositions of random plane waves), and level repulsion (Wigner–Dyson statistics).
Exceptional states called quantum scars (Heller 1984) concentrate probability along unstable periodic orbits — a quantum correction to classical ergodicity.