This monograph is based on the script of a lecture series on the quantum mechanics of classically chaotic systems given by the author at the University of Marburg during the summer term 1995. The lectures were attended by students with basic knowledge in quantum mechanics, including members of the author's own group working on microwave analogous experiments on quantum chaotic questions.

When preparing the lectures the author became aware that a comprehensive textbook, covering both the theoretical and the experimental aspects, was not available. The present monograph is intended to fill this gap.

The basic concepts of the quantum mechanics of classically chaotic systems, termed ‘quantum chaos’ for short, are easy to grasp by any student of physics. The mathematical apparatus needed, however, often tends to obscure the physical background. That is why the theoretical results will be illustrated by real experimental or numerical data whenever possible.

Chapter 1 gives a short introduction on the essential ideas of semiclassical quantum mechanics, which is illustrated by two examples taken from the microwave billiards and the kicked rotator.

Chapter 2 treats the different types of billiard experiments. Methods to study vibrating solids and liquids are presented. The main part of this chapter deals with microwave techniques, as by far the most experiments have been performed in microwave billiards. The chapter ends with a discussion of mesoscopic billiards including quantum corrals.

Chapter 3 introduces random matrix theory. It was developed in the sixties, and is treated in several reviews and monographs.