Quantum mechanical implications of classical ergodicity

The concept of quantum ergodicity is examined empirically through a quantitative study of the eigenfunctions of both the Barbanis and Casati--Ford potentials. By considering the behavior of the nodes of the wave functions and by employing a combination of natural orbital and spectral analyses, many of the higher eigenstates can apparently be classified as ergodic. These particular states seem to correspond quite well not only to classical ergodic trajectories but also to (currently) unquantizable semiclassical wave functions. The relationship between this quantal ergodicity and its classical equivalent is discussed