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A. Jüngel, J.-F. Mennemann:
"Time-dependent simulations of multidimensional quantum waveguides using a time-splitting spectral method";
in: "ASC Report 45/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5, 1 - 21.

The electron flow through quantum waveguides is modeled by the
time-dependent Schroedinger equation with absorbing boundary conditions,
which are realized by a negative imaginary potential. The Schroedinger
equation is discretized by a time-splitting spectral method, and the
quantum waveguides are fed by a mono-energetic incoming plane wave
pulse. The resulting algorithm is extremely efficient due to the Fast
Fourier Transform implementation of the spectral scheme. Numerical
convergence rates for a one-dimensional scattering problem are calculated.
The transmission rates of a two-dimensional T-stub quantum waveguide and a
single-branch coupler are numerically computed. Moreover, the transient
behavior of a three-dimensional T-stub waveguide is simulated.

http://www.asc.tuwien.ac.at/preprint/2009/asc45x2009.pdf