We study the Einstein relation for the diffusivity to mobility ratio (DMR) in quantum wires (QWs) of III-V, ternary, and quaternary materials in the presence of light waves, whose unperturbed energy band structures are defined by the three band model of Kane. It has been found, taking n-InAs, n-InSb, n-Hg1−xCdxTe, n-In1−xGaxAsyP1−y lattice matched to InP as examples, that the respective DMRs exhibit decreasing quantum step dependence with the increasing film thickness, decreasing electron statistics, increasing light intensity and wavelength, with different numerical values. The nature of the variations is totally band structure dependent and is influenced by the presence of the different energy band constants. The strong dependence of the DMR on both the light intensity and the wavelength reflects the direct signature of the light waves which is in contrast as compared to the corresponding QWs of the said materials in the absence of photoexcitation. The classical equation of the DMR in the absence of any field has been obtained as a special case of the present analysis under certain limiting conditions and this is the indirect test of the generalized formalism. We have suggested an experimental method of determining the DMR in QWs of degenerate materials having arbitrary dispersion laws and our results find six applications in the field of quantum effect devices.