Morphological image analysis of quantum motion in billiards.

Morphological image analysis is applied to the time evolution of the probability distribution of a quantum particle moving in two- and three-dimensional billiards. It is shown that the time-averaged Euler characteristic of the probability distribution provides a well defined quantity to distinguish between classically integrable and nonintegrable billiards. In three dimensions the time-averaged mean breadth of the probability distribution may also be used for this purpose.