corrections to Gutzwiller's trace formula for
systems with a smooth potential were presented. Here we present an extension
of that theory to systems with discrete symmetries. We apply the method to
the two-dimensional hydrogen atom in a uniform magnetic field and exploit
the 
-symmetry in the calculation of the correction terms. The
numerical results for the semiclassical values are compared with values
extracted from exact quantum mechanical calculations. The comparison shows
a very good agreement.
Key words: semiclassical theories, Gutzwiller's trace formula,
expansions, discrete symmetries, diamagnetic hydrogen atom
