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Zbl 1094.65088
Sun, Zhi-zhong; Wu, Xiaonan
The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions. (English)
[J] J. Comput. Phys. 214, No. 1, 209-223 (2006). ISSN 0021-9991

The authors analyze a difference scheme for a one-dimensional Schrödinger equation with nonreflecting boundary condition. It is required that the potential term be constant outside a compact interval. An energy method is used to prove stability of the method and to estimate its rate of convergence.
[Gerald W. Hedstrom (Pleasanton)]
MSC 2000:
*65M12 Stability and convergence of numerical methods (IVP of PDE)
65M06 Finite difference methods (IVP of PDE)
35Q40 PDE from quantum mechanics

Keywords: Schrödinger equation; nonreflecting boundary condition; finite difference; convergence; stability

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