  We formulate a set of conditions under which dynamics of a time-dependent
quantum Hamiltonian are integrable. The main requirement is the existence of a
nonabelian gauge field with zero curvature in the space of system parameters.
Known solvable multistate Landau-Zener models satisfy these conditions. Our
method provides a strategy to incorporate time-dependence into various quantum
integrable models, so that the resulting non-stationary Schrodinger equation is
exactly solvable. We also validate some prior conjectures, including the
solution of the driven generalized Tavis-Cummings model.
