We derive a formula which relates the QCD potentials in momentum space and in
position space in terms of the beta-function of the renormalization-group
equation for the potential. This formula is used to study the theoretical
uncertainties in the potential and in particular in its application to the
determination of the pole mass m_b when we use perturbative expansions. We
demonstrate the existence of these uncertainties for the Richardson potential
explicitly and then discuss the limited theoretical accuracy in the
perturbative QCD potential. We conclude that a theoretical uncertainty of m_b
much below 100 MeV would not be achievable within perturbative QCD.
