  The time-evolution operator for an explicitly time-dependent Hamiltonian is
expressed as the product of a sequence of unitary operators. These are obtained
by successive time-dependent unitary transformations of the Hilbert space
followed by the adiabatic approximation at each step. The resulting adiabatic
product expansion yields a generalization of the quantum adiabatic
approximation. Furthermore, it leads to an infinite class of exactly solvable
models.
