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L. Bian, G. Pang, S. Tang, A. Arnold:
"ALmost EXact boundary conditions for transient Schrödinger-Poisson system";
in: "ASC Report 3/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, ISBN: 978-3-902627-09-4, 1 - 21.

For the Schro¨dinger-Poisson system, we propose an ALmost EXact(ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflec-tions. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. The modulus of the wave function exhibits pronounced peaks at resonant values for the wave number. Hence, it is important to incorporate these modes when selecting the cut-off wave number for numerical simulations.

Schrödinger-Poisson simulation, ALEX boundary condition, resonant tunneling diode, primary peak, resonant wave numbers

http://www.asc.tuwien.ac.at/preprint/2016/asc3x2016.pdf