  The general method for treating non-Gaussian wave functionals in the
Hamiltonian formulation of a quantum field theory, which was previously
developed and applied to Yang--Mills theory in Coulomb gauge, is generalized to
full QCD. The Hamiltonian Dyson-Schwinger equations as well as the quark and
gluon gap equations are derived and analysed in the IR and UV momentum regime.
The back-reaction of the quarks on the gluon sector is investigated.
