  We propose some extensions of the quark potential model to hybrids, fit them
to the lattice data and use them for the purpose of calculating the masses,
root mean square radii and wave functions at the origin of the conventional and
hybrid charmonium mesons. We treat the ground and excited gluonic field between
a quark and an antiquark as in the Born-Oppenheimer expansion, and use the
shooting method to numerically solve the required Schr$\ddot{\textrm{o}}$dinger
equation for the radial wave functions; from these wave functions we calculate
the mesonic properties. For masses we also check through a Crank Nichelson
discretization. For hybrid charmonium mesons, we consider the exotic quantum
number states with $ J^{PC} = 0^{+ -}, 1^{- +}$ and $2^{+ -}$. We also compare
our results with the experimentally observed masses and theoretically predicted
results of the other models. Our results have implications for scalar form
factors, energy shifts, magnetic polarizabilities, decay constants, decay
widths and differential cross sections of conventional and hybrid mesons.
