A fully microscopic theory of electron spin relaxation by the
D'yakonov-Perel' type spin-orbit coupling is developed for a semiconductor
quantum well with a magnetic field applied in the growth direction of the well.
We derive the Bloch equations for an electron spin in the well and define
microscopic expressions for the spin relaxation times. The dependencies of the
electron spin relaxation rate on the lowest quantum well subband energy,
magnetic field and temperature are analyzed.Comment: Revised version as will appear in Physical Review