The study presents the Landauer formula and Green’s function approach for analysing the scattering processes in a system attached to infinite one-dimensional leads. The study involves the calculation of the retarded Green’s function in which the simple formula of a one-dimensional tight binding chain in presented. The study involves mathematical aspects of solving the Schrodinger equation in open systems with a view to developing new conceptual approaches to scattering theory. Efficient schemes to obtain scattering matrices from mean-field Hamiltonians are developed and these are implemented in new numerical codes.