A discrete Dirichlet-to-Neumann map, derived from the semi-discrete Schrödinger equation and approximated by rational functions, yields stable absorbing boundary conditions for 3D quantum dynamics simulations.
One should notice that the difference between the analytical so lution and the exact solution of the discrete model might not be small due to th e large grid spacing
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Absorbing boundary conditions for the time-dependent Schr\"odinger-type equations in $\mathbb R^3$
A discrete Dirichlet-to-Neumann map, derived from the semi-discrete Schrödinger equation and approximated by rational functions, yields stable absorbing boundary conditions for 3D quantum dynamics simulations.