of the ground-state longitudinal wave functions obtained from the invariant mass ansatz: $N_1\exp\big(-\frac{m^2_q}{2\kappa^2x(1-x)}\big)$ and from BLFQ: $N_2 \big( x(1-x)\big)^{2m^2_q/\kappa^2}$. We convert the wave functions to those of the Brodsky-de Téramond convention [@Brodsky:2014yha] by including a factor $\sqrt{x(1-x)}$ \[cf. Eq. ([\[eqn:normalization\]]{})\]. Quark mass $m_q$ and confining strength $\kappa$ are taken from the fits of Ref. [@Brodsky:2014yha] and this work (Sect. \[sect:numerical\_results\]). []{data-label="fig:longitudinal_basis_functions"}](Figures/longitudinal_basis){width="50.00000%"}

States may be identified according to their mass spectrum with the help of parity $\mathsf P$ and charge conjugation $\mathsf C$. The quarkonium ground state (1S) is identified with $n=0, m=0, l=0$: $$\psi_\mathrm{gs}(\vec k_\perp, x) = N \exp\big[ -\vec k^2_\perp/(2\kappa^2 x(1-x)) \big] \big( x(1-x)\big)^{2m^2_q/\kappa^2}.$$ In the literature, a commonly-used way to incorporate quark masses in the AdS/QCD wave function is through the invariant mass ansatz (IMA) [@Brodsky:2008pg], viz, $$N \exp\big[ -\vec k^2_\perp/(2\kappa^2 x(1-x)) \big] \; \to \; N' \exp\big[ -(\vec k^2_\perp+m_q^2)/(2\kappa^2 x(1-x)) \big].$$ Figure \[fig:longitudinal\_basis\_functions\] compares the purely longitudinal part of our ground-state wave function with that of the IMA wave function. Our longitudinal wave function becomes almost identical to the IMA wave function in both the chiral limit and the heavy quark limit, except near the endpoints. This reflects the fact that rotational symmetry is restored in the 