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 ($\text{qq}$) sources. We show that for separation between the sources less then a few fm the gluonic ground state of the static $\text{qq}$ system can be well described in terms of a mean field wave functional with the excited states corresponding to a single quasi-particle excitation of the gluon field. We also discuss the role of many particle excitations relevant for large separation between sources.