Quantum kinetic equations (QKE) are used for the description of highly excited electrons in the conduction band of semiconductors in the short time regime. The relaxation process is described with QKE in Born approximation and with QKE including two particle correlations. The results of the approximations are compared for different particle densities with the exact solution of a one-dimensional model of N electrons with linear dispersion interacting with optical phonons. Especially the discussion of the processes contributing to the gain peak allows a better understanding of the approximations.