We present ab initio calculations for both the wave functions and the energ
ies of single quasiparticles. The conventional quasiparticle approach evalu
ates energy-level corrections to first order in the difference between the
self-energy and the Kohn-Sham exchange-correlation potential. Here,we also
recalculate the quasiparticle states. At the example of the GaAs(110) surfa
ce we show that this nonperturbative treatment is important far surfaces wi
th electronic states close in energy but different with respect to their lo
calization. As a sensitive observable the reflectance anisotropy is studied
. [S0163-1829(99)15947-2].