  The Zeeman splitting and the underlying value of the g-factor for conduction
band electrons in GaAs/Al_xGa_{1-x}As quantum wells have been measured by
spin-beat spectroscopy based on a time-resolved Kerr rotation technique. The
experimental data are in good agreement with theoretical predictions. The model
accurately accounts for the large electron energies above the GaAs conduction
band bottom, resulting from the strong quantum confinement. In the tracked
range of optical transition energies E from 1.52 to 2.0eV, the electron
g-factor along the growth axis follows closely the universal dependence
g_||(E)= -0.445 + 3.38(E-1.519)-2.21(E-1.519)^2 (with E measured in eV); and
this universality also embraces Al_xGa_{1-x}As alloys. The in-plane g-factor
component deviates notably from the universal curve, with the degree of
deviation controlled by the structural anisotropy.
