  Real atomic systems, like the hydrogen atom in a magnetic field or the helium
atom, whose classical dynamics are chaotic, generally present both discrete and
continuous symmetries. In this letter, we explain how these properties must be
taken into account in order to obtain the proper (i.e. symmetry projected)
$\hbar$ expansion of semiclassical expressions like the Gutzwiller trace
formula. In the case of the hydrogen atom in a magnetic field, we shed light on
the excellent agreement between present theory and exact quantum results.
