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One of the major difficulties in solving the coupled Schrödinger–Poisson equations for open quantum systems is providing the wave functions for a large energy set. In this context, the R-matrix formalism provides an alternative method to obtain efficiently the wave functions. In a first step, which is energy independent, the eigenvalue problem associated with the quantum system is solved only once using fixed boundary conditions. Then, in a second step, the wave functions and transmission coefficients are obtained with a much lower computational effort for each energy. As an application, self-consistent potential and charge distribution, as well as the ballistic source-drain conductance, are calculated for a cylindrical nanowire transistor. The numerical accuracy with respect to basis cardinality is also discussed.