A short historical overview is given on the development of our knowledge of
complex dynamical systems with special emphasis on ergodicity and chaos, and on
the semiclassical quantization of integrable and chaotic systems. The general
trace formula is discussed as a sound mathematical basis for the semiclassical
quantization of chaos. Two conjectures are presented on the basis of which it
is argued that there are unique fluctuation properties in quantum mechanics
which are universal and, in a well defined sense, maximally random if the
corresponding classical system is strongly chaotic. These properties constitute
the quantum mechanical analogue of the phenomenon of chaos in classical
mechanics. Thus quantum chaos has been found.Comment: 12 pages; uuencoded compressed tar file containing PostScript source;
PostScript file also available by anonymous ftp to ftp.desy.de as
/pub/preprints/desy/1994/desy-013.p
