2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/24051Using 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, $d \hatρ/dt \neq 0$. 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.RevTex 3 Pages in double column; no figureOther Condensed Mattertext