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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 firstdoi:10.1088/1742-6596/639/1/012014 fatcat:cs2evmkkujfhhfqvymbpncfcwu