Within the non-relativistic quark model framework, the spectra for $c\bar{c}$-mesons are usually derived through the (numerical) solution of the Schrödinger equation with a given potential for quark-antiquark interactions. Cornell potential plus hyperfine corrections are popular models with successful predictions of mass spectra of these heavy mesons. We use the Numerov matrix method to obtain the mass spectra of $c\bar{c}$-mesons with high accuracy. Their (root-mean-squared) radii $r_{\text{rms}}$ are then derived through the corresponding radial wavefunctions. Angular momentum quantum numbers and $r_{\text{rms}}$ allow to determine the momentum width for these meson states. We then relate the masses and $r_{\text{rms}}$ for $c\bar{c}$-mesons through constraints arising from the uncertainty and variational principles. These ideas can be straightforwardly generalized for other meson states.