A quantum explanation based on the previous semi-classical theory has
been presented for the giant magnetoresistance (GMR) effect in this le
tter. A simple model Hamiltonian has been proposed for the conduction
electrons in the magnetic layered structures in which the interaction
of the conduction electrons with the local spins and the spin-dependen
t scattering potential have been considered, then an analytical expres
sion of the effective electric conductivity is derived after some simp
lifying procedures. The main feature of the GMR effect may be explaine
d by this simple model qualitatively.