Despite the tremendous awareness of Rayleigh scattering characteristics and its considerable research interest for numerous fields, no report has been documented on the dynamic characteristics of spectrum evolution (SpE) and physical law for Rayleigh scattering from a micro perspective. Herein, the dynamic characteristics of the SpE of Rayleigh scattering in a one-dimensional waveguide (ODW) is investigated based on the quantum theory and a SpE-model of Rayleigh backscattering (RBS) source is established. By means of simulation, the evolution law which represents the dynamic process of the spectrum linewidth at a state of continuous scattering is revealed, which is consistent with our previous experimental observation. Moreover, an approximate theoretical prediction of the existing relationship between the spectrum linewidth of RBS source and the transmission length in ODW is proposed, which theoretically provides the feasibility of constructing functional devices suitable to ascertain laser linewidth compression. The designed experimental scheme can be implemented provided the assumptions are fulfilled. In addition, a theoretical model of the micro-cavity structure to realize the deep compression of laser linewidth is proposed.