In short-wave asymptotics one studies approximate solutions to wave equations that are valid in the limit of small wave lengths. One example is the semiclassical approximation in quantum mechanics. It is an approximation that connects wave properties to the trajectories of Newtonian mechanics. This is analogous to the geometrical optics approximation for electro-magnetic waves, that expresses wave properties in terms of rays.
Semiclassical approximations are one of the major tools in the field of quantum chaos .
They provide a link between quantum mechanics and classical mechanics, and thus they allow to study how these theories are connected. These effects require the inclusion of the next-order correction to the leading order approximation for short wave lengths. For this reason, there has been recently an increased interest in diffraction effects in quantum systems. One project involves the study of the consequences of adding one and more point-like objects to a quantum system. Statistical distributions of energy levels One of the central topics in quantum chaos is the random matrix hypothesis.