The energy bound-state solutions of the spinless Salpeter equation (SSE) have been obtained under a spin-dependent Cornell potential function via the Wentzel–Kramers–Brillouin approximation. The energy levels were applied to predict the mass spectra for the charmonium, bottomonium, and bottom-charmed mesons. The relativistic corrections for the angular momentum quantum number l>0l\gt 0, total angular momentum quantum numbers j=l,j=l±1j=l,\hspace{.3em}j=l\pm 1, and the radial quantum numbers n = 1–4 improve the mass spectra. The results agree fairly with experimental data and theoretic results reported in existing works, where the authors utilized different forms of the inter-quark potentials and methods. The deviation of the obtained masses for the charmonium and bottomonium from the observed data yields a total percentage error of 3.32 and 1.11%, respectively. The results indicate that the accuracy of the masses is correlated with the magnitude of masses for the charm and bottom quarks. The SSE together with the phenomenological spin-dependent Cornell potential provides an adequate account of the mass spectroscopy for the heavy mesons and may be used to predict other spectroscopic parameters.
