Efficient computation of Wigner–Eisenbud functions

The RR-matrix method, introduced by Wigner and Eisenbud (1947) [1], has been applied to a broad range of electron transport problems in nanoscale quantum devices. With the rapid increase in the development and modeling of nanodevices, efficient, accurate, and general computation of Wigner–Eisenbud functions is required. This paper presents the Mathematica package WignerEisenbud, which uses the Fourier discrete cosine transform to compute the Wigner–Eisenbud functions in dimensionless units for an arbitrary potential in one dimension, and two dimensions in cylindrical coordinates.Program summaryProgram title: WignerEisenbudCatalogue identifier: AEOU_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOU_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlDistribution format: tar.gzProgramming language: MathematicaOperating system: Any platform supporting Mathematica 7.0 and aboveKeywords: Wigner-Eisenbud functions, discrete cosine transform (DCT), cylindrical nanowiresClassification: 7.3, 7.9, 4.6, 5Nature of problem:Computing the 1D and 2D Wigner–Eisenbud functions for arbitrary potentials using the DCT.Solution method:The R-matrix method is applied to the physical problem. Separation of variables is used for eigenfunction expansion of the 2D Wigner–Eisenbud functions. Eigenfunction computation is performed using the DCT to convert the Schrödinger equation with Neumann boundary conditions to a generalized matrix eigenproblem.Limitations:   Restricted to uniform (rectangular grid) sampling of the potential. In 1D the number of sample points, nn, results in matrix computations involving n×nn×n matrices.Unusual features:Eigenfunction expansion using the DCT is fast and accurate. Users can specify scattering potentials using functions, or interactively using mouse input. Use of dimensionless units permits application to a wide range of physical systems, not restricted to nanoscale quantum devices.Running time: Case dependent.