The density matrix is solved more rigorously, compared with the third-order pertubation method used in the conventional theory, for a semiconductor laser amplifier. Then the coupled wave equations are derived to explain the wavelength conversion due to the spectral hole burning in the semiconductor optical amplifier. It is shown that our results can explain the effect of saturation of the population density on the electric polarization, which affects the four-wave mixing and wavelength conversion, better than the conventional theroy where the third-order pertubation is used.