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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Approximation and Fast Calculation of Non-local Boundary Conditions for the Time-dependent Schrödinger Equation
verfasst von : Anton Arnold, Matthias Ehrhardt, Ivan Sofronov
Erschienen in: Domain Decomposition Methods in Science and Engineering
Verlag: Springer Berlin Heidelberg
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We present a way to efficiently treat the well-known transparent boundary conditions for the Schrödinger equation. Our approach is based on two ideas: firstly, to derive a discrete transparent boundary condition (DTBC) based on the Crank-Nicolson finite difference scheme for the governing equation. And, secondly, to approximate the discrete convolution kernel of DTBC by sum-of-exponentials for a rapid recursive calculation of the convolution. We illustrate the efficiency of the proposed method on several examples.
A much more detailed version of this article can be found in Arnold et al. [2003].