A theory is presented of induced Raman emission in a three‐level system whose parameters are appropriate for microwave to optical frequencies. Solutions of the time‐dependent Schro¨dinger equation are obtained for arbitrary intensity of the pump and signal radiations, which are assumed to be not too many line‐widths off resonance. It is shown how the quantum‐mechanical aspects of the problem may be separated from the statistical‐mechanical aspects, in contrast to the density matrix techniques. The frequency dependence of the Raman emission on the frequency and intensity of the pumping radiation obtained by this method is presented and compared with the results we have obtained by other methods. The intensity and line shape of the Raman emission when the pump frequency is far off resonance are also obtained. The case of three interacting fields is also considered.