  We derive the planar large N non-supersymmetric background of the quantum
mechanical hamiltonian of two hermitean matrices coupled via a Yang-Mills
interaction, in terms of the density of eigenvalues of one of the matrices.
This background satisfies an implicit non linear integral equation, with a
perturbative small coupling expansion and a solvable large coupling solution,
which is obtained. The energy of system and the expectation value of several
correlators are obtained in this strong coupling limit. They are free of
infrared divergences.
