  We derive contributions to the trace formula for the spectral density
accounting for the role of diffractive orbits in two-dimensional billiard
systems with corners. This is achieved by using the exact Sommerfeld solution
for the Green function of a wedge. We obtain a uniformly valid formula which
interpolates between formerly separate approaches (the geometrical theory of
diffraction and Gutzwiller's trace formula). It yields excellent numerical
agreement with exact quantum results, also in cases where other methods fail.
