The exact diagonalization of the kinetic energy-term of the QCD-Hamiltonian, at low energy and restricted to a finite volume, is resumed. The Coulomb interaction term, approximated by a sum of a 1/r and a linear potential, is added. Only quarks and anti-quarks are considered, while the gluons are taken into account effectively via the linear potential. The Tamm-Dankoff method is applied to obtain the meson spectrum of a simplified QCD- Hamiltonian at low energy. The current status and first results of our research-program are presented.