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We study the statistical properties of wave scattering in a disorderedwaveguide. The statistical properties of a "building block" of length (delta)Lare derived from a potential model and used to find the evolution with lengthof the expectation value of physical quantities. In the potential model thescattering units consist of thin potential slices, idealized as delta slices,perpendicular to the longitudinal direction of the waveguide; the variation ofthe potential in the transverse direction may be arbitrary. The sets ofparameters defining a given slice are taken to be statistically independentfrom those of any other slice and identically distributed. In thedense-weak-scattering limit, in which the potential slices are very weak andtheir linear density is very large, so that the resulting mean free paths arefixed, the corresponding statistical properties of the full waveguide dependonly on the mean free paths and on no other property of the slice distribution.The universality that arises demonstrates the existence of a generalizedcentral-limit theorem.  Our final result is a diffusion equation in the space of transfer matrices ofour system, which describes the evolution with the length L of the disorderedwaveguide of the transport properties of interest. In contrast to earlierpublications, in the present analysis the energy of the incident particle isfully taken into account.Comment: 75 pages, 10 figures, submitted to Phys. Rev

Statistical scattering of waves in disordered waveguides: From microscopic potentials to limiting macroscopic statistics