We justify the use of harmonic oscillator eigenfunctions for expanding the fermionic fields of an effective field theory and evaluate its utility for solving a Hamiltonian inspired by the QCD formalism in the Coulomb Gauge. Since the functions involved in such expansion are non-relativistic, the Talmi-Moshinsky transformations can be used to recover the translational invariance of the center of mass of the mesonic states. Finally, many-body methods and an a posteriori flavor mixing procedure are used to compute a preliminary spectrum for the mesons below 1 GeV.