Q},R\rangle$ excites any number of gluons and couples them to the quark sources. The Coulomb energy was defined as the expectation value, $V_C$ in $|Q{\bar Q},R\rangle$ minus the vacuum energy and it is therefore different from the phenomenological static potential energy which corresponds to the total energy (measured with respect to the vacuum) of the true eigenstate of the Hamiltonian with a $Q{\bar Q}$ pair. If one defines [@goz] $$\begin{aligned}
G(R,T) &\equiv  \langle Q{\bar Q},R|e^{-(H-E_0)T}|Q{\bar Q},R\rangle 
 \nonumber \\
& = \sum_n |\langle Q {\bar Q},R,n|Q{\bar Q},R\rangle|^2 e^{-(E_n -
 E_0) T},\end{aligned}$$ then the Coulomb potential on the lattice can be calculated from $$V_C(R) = \lim_{T=0} -{d\over {dT}} \log(G(R,T)),$$ and the phenomenological potential from $$V(R) = \lim_{T=\infty} -{d\over {dT}} \log(G(R,T)).$$ Thus one should be comparing $V_C(R)$ in [Eq. (\[vc\])]{} to the lattice Coulomb potential and not to the phenomenological potential obtained from the Wilson loop. Finally, one could try to optimize the state with sources, [*e.g.*]{} by adding gluonic components. In this case terms in the Hamiltonian beyond the Coulomb term would contribute to the energy of the system and one could compare with the true (Wilson loop) static energy. In our previous studies, where we extracted numerical values for $\mu$ and 