Integrable Time-Dependent Quantum Hamiltonians

We formulate a set of conditions under which the nonstationary Schrodinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abel ian 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 while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.