We have carried out the calculation of the spectrum of heavy quark mesons (charmonium and bottomonium) following an alternative strategy to solve the fundamental QCD Lagrangian based on the «effective» Lagrangian of ACD, Anisotropic Chromo Dynamics. An «ab initio» calculation of the interaction Hamiltonian, involving the quark massesmc andmb, the string tension μ and the QCD coupling constant\(\alpha _s \) is presented, together with the numerical results of the solution of a relativistic Schrodinger equation containing such interaction. The agreement with existing data is quite satisfactory.