On the nonrelativistic dynamics of heavy particles near the production threshold

A solution to the Schrodinger equation for the nonrelativistic Green function which is used for describing the heavy quark-antiquark pair production near the threshold in $e^{+}{e}^{-}$ annihilation is presented. A quick comparison with existing results is given. A choice of the effective mass scale for the nonrelativistic system with Coulomb interaction is discussed.