  We compute masses of bottomonium and charmonium bound states using a
Schr\"odinger equation with a heavy quark-antiquark potential including $1/m$
and $1/m^2$ corrections previously derived in potential Non-Relativistic QCD
and computed with lattice QCD. This is a preparatory step for a future project,
where we plan to take into account similar corrections to study quarkonium
resonances and tetraquarks above the lowest meson-meson thresholds.
