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Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential. (English) Zbl 1161.65074

Summary: Mathematical constructions and comparisons of accurate absorbing boundary conditions for the one-dimensional Schrödinger equation with a general variable repulsive potential are developed. Stable semi-discretization schemes are built for the associated initial boundary value problems. Finally, some numerical simulations give a comparison of the various absorbing boundary conditions and show that they yield accurate computations.

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
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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