2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141766We introduce a novel method to find exact density operators for a spin-1/2 particle in time-dependent magnetic fields by using the one-mode bosonic representation of $su(2)$ and the connection with a time-dependent oscillator. As illustrative examples, we apply the method to find the density operators for constant and/or oscillating magnetic fields, which turn out to be time-dependent in general.RevTex, 14 pages, no figureQuantum Physicstext