[en] Inequalities are established on the energy levels of two-particle systems interacting via the same potential with different masses and different angular momenta. When this is applied to the J/psi and UPSILON particles, one gets an inequality on the mass difference between the heavy quark and the charmed quark as a function of the masses of the J/psi, the UPSILON and the UPSILON'. The authors find Msub(b)-msub(c) > 3.29 GeV. In the appendix, a concavity property of the energy levels as a function of the angular momenta is discussed. This property also implies 2Esub(p)>Esub(1S)+Esub(2S), which gives for the mean mass of the P states of UPSILON a lower limit of 9.76 GeV. (Auth.)