We begin by discussing the properties expected of eigenfunctions of a classically chaotic Hamiltonian system, using simple Correspondence Principle arguments. The properties involve nodal surfaces, coordinate and momentum space amplitude distribution, and phase space distribution. The eigenfunctions of the stadium billiard are examined, and it is found that the periodic orbits of shortest periods and smallest stability parameter profoundly affect the eigenfunctions: “scars” of higher wavefunction density surround the special periodic orbits. Finally a theory is presented for the scars, showing that they must exist, and relating them directly to the special periodic orbits. These same periodic orbits cause level density fluctuations.

%B Quantum Chaos and Statistical Nuclear Physics: Proceedings of the 2nd International Conference on Quantum Chaos and the 4th International Colloquium on Statistical Nuclear Physics, Held at Cuernavaca, México, January 6–10, 1986 %I Springer Berlin Heidelberg %P 162–181 %G eng %U http://link.springer.com/chapter/10.1007%2F3-540-17171-1_15 %R 10.1007/3-540-17171-1_15