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.
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