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Manuscript Title: A general spectral method for the numerical simulation of one-dimensional interacting fermions
Authors: Christian Clason, Gregory von Winckel
Program title: assembleFermiMatrix
Catalogue identifier: AEKO_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 183(2012)405
Programming language: MATLAB.
Computer: Any architecture supported by MATLAB.
Operating system: Any supported by MATLAB; tested under Linux (x86-64) and Mac OS X (10.6).
RAM: Depends on the data
Keywords: Schrödinger equation, Fermions, Numerical solution, Spectral method.
Classification: 4.3, 2.2.

Nature of problem:
The direct numerical solution of the multi-particle one-dimensional Schrödinger equation in a quantum well is challenging due to the exponential growth in the number of degrees of freedom with increasing particles.

Solution method:
A nodal spectral Galerkin scheme is used where the basis functions are constructed to obey the antisymmetry relations of the fermionic wave function. The assembly of these matrices is performed efficiently by exploiting the combinatorial structure of the sparsity patterns.

Restrictions:
Only one-dimensional computational domains with homogeneous Dirichlet or periodic boundary conditions are supported.

Running time:
Seconds to minutes