Quantum Chaos: An Exploration of the Stadium Billiard Using Finite Differences
نویسندگان
چکیده
We investigate quantum chaos in chaotic billiards by modelling the square (non-chaotic) and the stadium (chaotic) billiards as 2D infinite square wells. We developed MATLAB code that uses grid points and the method of finite differences to numerically solve the Schrödinger equation for either case. We successfully obtained the “scar” structures in higher energy eigenfunctions for the stadium case, discovered by Joseph Heller in 1984. We also studied the eigenvalue spacings, and obtained the Poisson distribution for the square case and the GOE distribution for the chaotic case. Thus, we were able to demonstrate both features (scarring in eigenfunctions and GOE distribution in eigenvalue separation) that indicate the presence of chaos in the classical limit.
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