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Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrödinger equation. (English) Zbl 1037.65097

The paper deals with the problem of constructing stable approximation schemes for the one-dimensional linear Schrödinger equation set in an unbounded domain. Futhermore some unconditionally stable discretization schemes are developed for the initial-boundary value problem in a bounded domain with a transparent boundary condition. The authors address two possible choices of transparent boundary conditions based on the Dirichlet-Neumann and Neumann-Dirichlet operators. Some numerical experiments are presented.

MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35Q40 PDEs in connection with quantum mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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