  Motivated by the present interest in the heavy quark effective theory, we use
the spectator equation to treat the mesonic bound states of heavy quarks. The
kernel we use is based on scalar confining and vector Coulomb potentials. Wave
functions are treated to leading order and energies to order $1/m_Q$ in the
heavy-light systems, and order $1/m_Q^2$ in heavy-heavy systems. Our results
are in reasonable agreement with experimental measurements. We estimate two of
the parameters of the heavy quark effective theory, and propose further
calculations that may be undertaken in the future.
