The charge transport is one of the most important factors for the efficiency in nanostructured devices. The detailed nature of transport processes in these systems is still not completely resolved. Starting from the Drude model, we have proposed an analytical method for describing classically the most important quantities concerning transport phenomena, i.e. the velocity correlation functions, the mean square deviation of position and the diffusion coefficient. To fully account for quantum effects arising in systems of reduced dimensions, in this work we present the quantum mechanical version of this model, comprehending the oscillator strength weights, and apply the model to single-walled carbon nanotube ﬁlms, extracting the oscillator weights from reflectivity data reported in the literature. We are able to give a complete and precise description of time correlations avoiding time-consuming numerical or simulation procedures. This method demonstrates high generality and offers perspectives even in the study of ions, like mass transfer, and solutions, so as in nano bio systems. This quantum mechanical extension allows significant applications for the nanodiffusion in nanostructured, porous and cellular materials, as for biological, medical and nanopiezotronic devices.