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A. Jüngel, J.-F. Mennemann:
"Time-dependent simulations of quantum waveguides using a time-splitting spectral method";
Mathematics and Computers in Simulation, 81 (2010), 883 - 898.

The electron flow through quantum waveguides is modeled by the time-dependent Schrödinger equation with absorbing boundary
conditions, which are realized by a negative imaginary potential. The Schrödinger 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 FourierTransform 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.

Siehe englisches Abstract.

Schroedinger equation; absorbing boundary conditions; quantum waveguide