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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_0Distribution 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. |

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