  In this paper we propose a particular description of meson spectroscopy, with
emphasis in heavy bound states like charmonia and bottomonia, after working on
the main aspects of the construction of an effective potential model. We use
the prerogatives from ``soft QCD'' to determine the effective potential terms,
establishing the asymptotic Coulomb term from one gluon exchange approximation.
At the same time, a linear confinement term is introduced in agreement with QCD
and phenomenological prescription. The main aspect of this work is the
simplification in the calculation, consequence of a precise and simplified
description of the kinetic term of the Hamiltonian. With this proposition we
perform the calculations of mass spectroscopy for charmonium and bottomonium
mesons and we discuss the real physical possibilities of developing a
generalized potential model, its possible advantages relative to experimental
parameterization and complexity in numerical calculations.
