  We develop a mechanism to build the light-front wavefunctions (LFWFs) of
meson bound states on a small-sized basis function representation. Unlike in a
standard Hamiltonian formalism, the Hamiltonian in this method is implicit, and
the information of the system is carried directly by the functional form and
adjustable parameters of the LFWFs. In this work, we model the LFWFs for four
charmonium states, $\eta_c$, $J/\psi$, $\psi'$, and $\psi(3770)$ as
superpositions of orthonormal basis functions. We choose the basis functions as
eigenfunctions of an effective Hamiltonian, which has a longitudinal confining
potential in addition to the transverse confining potential from light-front
holographic QCD. We determine the basis function parameters and superposition
coefficients by employing both guidance from the nonrelativistic description of
the meson states and the experimental measurements of the meson decay widths.
With the obtained wavefunctions, we study the features of those meson states,
including charge radii and parton distribution functions. We use the $J/\psi$
LFWF to calculate the meson production in diffractive deep inelastic scattering
and ultra-peripheral heavy-ion collisions, and the $\eta_c$ LFWF to calculate
its diphoton transition form factor. Both results show good agreement with
experiments. The obtained LFWFs have simple-functional forms and can be readily
used to predict additional experimental observables.
