Quantum Scars — Stadium Billiard
Semiclassical wavefunctions enhanced along unstable periodic orbits in a chaotic billiard
Eigenstate
Eigenstate index n:
12
Stadium ratio a/R:
1.00
Hbar (semiclassical):
0.08
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Animate Eigenstates
(-ℏ²/2m)∇²ψ = Eψ inside Ω
ψ|∂Ω = 0 (Dirichlet BC)
Scar: |ψ|² ↑ near periodic orbit
Quantum scars (Heller 1984): in classically chaotic billiards, certain quantum eigenstates show anomalously large probability density along unstable classical periodic orbits — defying ergodic expectations.