  The spatial self-organization of a Bose-Einstein condensate (BEC) in a
high-finesse linear optical cavity is discussed. The condensate atoms are
laser-driven from the side and scatter photons into the cavity. Above a
critical pump intensity the homogeneous condensate evolves into a stable
pattern bound by the cavity field. The transition point is determined
analytically from a mean-field theory. We calculate the lowest lying Bogoliubov
excitations of the coupled BEC-cavity system and the quantum depletion due to
the atom-field coupling.
