Open Access
March 2004 Exact artificial boundary conditions for the Schrödinger equation in $R ^2$
Houde Han, Zhongyi Huang
Commun. Math. Sci. 2(1): 79-94 (March 2004).


In this paper, we propose a class of exact artificial boundary conditions for the numerical solution of the Schrödinger equation on unbounded domains in two-dimensional cases. After we introduce a circular artificial boundary, we get an initial-boundary problem on a disc enclosed by the artificial boundary which is equivalent to the original problem. Based on the Fourier series expansion and the special functions techniques, we get the exact artificial boundary condition and a series of approximating artificial boundary conditions. When the potential function is independent of the radiant angle θ, the problem can be reduced to a series of one-dimensional problems. That can reduce the computational complexity greatly. Our numerical examples show that our method gives quite good numerical solutions with no numerical reflections.


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Houde Han. Zhongyi Huang. "Exact artificial boundary conditions for the Schrödinger equation in $R ^2$." Commun. Math. Sci. 2 (1) 79 - 94, March 2004.


Published: March 2004
First available in Project Euclid: 21 August 2009

zbMATH: 1089.35524
MathSciNet: MR2082820

Keywords: artificial boundary condition , Schrödinger equation , unbounded domain

Rights: Copyright © 2004 International Press of Boston

Vol.2 • No. 1 • March 2004
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