Coulomb energy and gluon distribution in the presence of static sources

We compute the energy of the ground state and a low-lying excitation of the gluonic field in the presence of static quark-anti-quark ($q\overline{q}$) sources. We show that for separation between the sources less then a few fm the gluonic ground state of the static $q\overline{q}$ system can be well described in terms of a mean field wave functional with the excited states corresponding to a single quasiparticle excitation of the gluon field. We also discuss the role of many particle excitations relevant for large separation between sources.