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Manuscript Title: Efficient Computation of Wigner-Eisenbud Functions
Authors: Bahaaudin M. Raffah, Paul C. Abbott
Program title: WignerEisenbud
Catalogue identifier: AEOU_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 184(2013)1581
Programming language: Mathematica 7.0.
Computer: All capable of running Mathematica.
Operating system: All capable of running Mathematica.
Keywords: Wigner-Eisenbud functions, Discrete cosine transform (DCT), Cylindrical nanowires.
PACS: 73.20.Dx, 31.15.-p.
Classification: 4.6, 5, 7.3, 7.9.

Nature 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 generalised matrix eigenproblem.

Restrictions:
Restricted to uniform (rectangular grid) sampling of the potential. In 1D the number of sample points, n, results in matrix computations involving n x 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:
The notebook provided takes under a minute to run.