Approximation and fast calculation of non-local boundary conditions for the time-dependent Schrödinger equation
Please always quote using this URN:urn:nbn:de:0296-matheon-932
- 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.
Author: | Anton Arnold, Matthias Ehrhardt, Ivan Sofronov |
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URN: | urn:nbn:de:0296-matheon-932 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2004/02/17 |
Release Date: | 2004/02/16 |
Institute: | Technische Universität Berlin |
Preprint Number: | 85 |