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A theoretical investigation of traveling wave light amplification in a GaAs double heterostructure device is presented in this paper. The analysis is self-consistent, semiclassical, and uses a density matrix formulation. Phenomenological constants are included to account for intraband relaxation processes, pumping, and spontaneous emission. The analysis is significantly different from previous rate equation approaches in that saturation effects are inherent in the results and phase information, important for coherent applications, is retained. Results presented for steady-state and pulsed operation include gain, pulse compression, multipulse effects, and the phase variation that occurs over the pulse time.