  The Dyson-Schwinger equations arising from minimizing the vacuum energy
density in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge are
solved numerically. A new solution is presented which gives rise to a strictly
linearly rising static quark potential and whose existence was previously
observed in the infrared analysis of the Dyson-Schwinger equations. For the new
solution we also present the static quark potential and calculate the running
coupling constant from the ghost-gluon vertex.
