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The transfer-matrix methodology is used to solve linear systems ofdifferential equations, such as those that arise when solving Schr\"odinger'sequation, in situations where the solutions of interest are in the continuouspart of the energy spectrum. The technique is actually a generalization inthree dimensions of methods used to obtain scattering solutions in onedimension. Using the layer-addition algorithm allows one to control thestability of the computation and to describe efficiently periodic repetitionsof a basic unit. This paper, which is an update of an article originallypublished in Physical and Chemical News 16, 46-53 (2004), provides apedagogical presentation of this technique. It describes in details how theband structure associated with an infinite periodic medium can be extractedfrom the transfer matrices that characterize a single basic unit. The method isapplied to the calculation of the transmission and band structure of electronssubject to cosine potentials in a cylindrical wire. The simulations show thatbound states must be considered because of their impact as sharp resonances inthe transmission probabilities and to remove unphysical discontinuities in theband structure. Additional states only improve the completeness of therepresentation.

Band-structure and electronic transport calculations in cylindrical wires : the issue of bound states in transfer-matrix calculations