  We construct a solution to the equation of motion of Hamiltonian lattice QCD
in the strong coupling limit using Wilson fermions which exactly diagonalizes
the Hamiltonian to second order in the field operators. This solution obeys the
free lattice Dirac equation with a dynamical mass which is identified with the
gap. The equation determining this gap is derived and it is found that the
dynamical quark mass is a constant to lowest order in N_c but becomes momentum
dependent once 1/N_c corrections are taken into account. We interpret our
solution within the framework of the N-quantum approach to quantum field theory
and discuss how our formalism may be systematically extended to study bound
states at finite temperature and chemical potential.
