Analytical expressions for the quantized energy levels in quantum wells, the optical gain, the differential optical gain, and the linewidth enhancement factor are presented based on a simple parabolic-band gain model. Explicit formulas show clearly the dependence of these factors on well width, doping, and photon energy. The optical gain in the form of g=g/sub 0/ In(N/N/sub 0/) is derived using explicit approximations in the Fermi functions, where g/sub 0/ is the proportionality constant, N is the injected carrier density, and N/sub 0/ is the transparency carrier density. The approximate formulas are shown to provide not only an efficient way of computing the gain-related parameters but also a convenient way of getting physical insights into the overall interplay of quantum well parameters.