Quantum Billiards: Stadium

Wave function probability density |ψ|² in a Bunimovich stadium billiard. Quantum scars trace classical periodic orbits even in a classically chaotic system.

n = 12
a = 1.00
plasma

The stadium billiard (two semicircles + rectangle) has fully chaotic classical dynamics. Quantum mechanically, certain eigenstates "scar" along unstable periodic orbits — Heller (1984). Use approximate modes via standing-wave superpositions fitted to the stadium boundary.