  We present a comprehensive semiclassical investigation of the
three-dimensional Sinai billiard, addressing a few outstanding problems in
"quantum chaos". We were mainly concerned with the accuracy of the
semiclassical trace formula in two and higher dimensions and its ability to
explain the universal spectral statistics observed in quantized chaotic
systems. For this purpose we developed an efficient KKR algorithm to compute an
extensive and accurate set of quantal eigenvalues. We also constructed a
systematic method to compute millions of periodic orbits in a reasonable time.
Introducing a proper measure for the semiclassical error and using the quantum
and the classical databases for the Sinai billiards in two and three
dimensions, we concluded that the semiclassical error (measured in units of the
mean level spacing) is independent of the dimensionality, and diverges at most
as log \hbar. This is in contrast with previous estimates. The classical
spectrum of lengths of periodic orbits was studied and shown to be correlated
in a way which induces the expected (random matrix) correlations in the quantal
spectrum, corroborating previous results obtained in systems in two dimensions.
These and other subjects discussed in the report open the way to extending the
semiclassical study to chaotic systems with more than two freedoms.
