  Using the invariant operator method for an effective Hamiltonian including
the radiation-spin interaction, we describe the quantum theory for
magnetization dynamics when the spin system evolves nonadiabatically and out of
equilibrium, $d \hat{\rho}/dt \neq 0$. It is shown that the vector parameter of
the invariant operator and the magnetization defined with respect to the
density operator, both satisfying the quantum Liouville equation, still obey
the Landau-Lifshitz-Gilbert equation.
