Efficient computation of WignerEisenbud functions ?
The R R -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 WignerEisenbud functions is required. This paper presents the Mathematica package WignerEisenbud, which uses the Fourier discrete cosine transform to compute the WignerEisenbud functions in dimensionless units for an arbitrary potential in one dimension, and two dimensions in cylindrical coordinates. Program title: WignerEisenbud Catalogue identifier: AEOU_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOU_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html Distribution format: tar.gz Programming language: Mathematica Operating system: Any platform supporting Mathematica 7.0 and above Keywords: Wigner-Eisenbud functions, discrete cosine transform (DCT), cylindrical nanowires Classification: 7.3, 7.9, 4.6, 5 Nature of problem: Computing the 1D and 2D WignerEisenbud 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 WignerEisenbud functions. Eigenfunction computation is performed using the DCT to convert the Schrdinger 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, n n , results in matrix computations involving nn n  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.
wignereisenbud functions discrete cosine transform (dct) cylindrical nanowires semiconductor heterostructures quantum transport