Large-Nclassical solution for the one-matrix model

Large-$N$ quantum systems are known to be dominated by a single classical solution $M_{\mathrm{ab}}$, which is the reduced transition matrix among the ground state and relevant "generalized-adjoint" eigenstates. For the one-matrix model, we obtain $M_{\mathrm{ab}}$ (and hence the spectrum) for transitions among the ground state and high-lying adjoint states. The method of solution is a new "quasiclassical" quantum mechanics, with no penetration of classically forbidden regions—yet another classical aspect of the large-$N$ limit.