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The stability and convergence of a difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions. (English) Zbl 1094.65088
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.
MSC:
65M12Stability and convergence of numerical methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
35Q40PDEs in connection with quantum mechanics