An Exact Absorbing Boundary Condition for the Schrödinger Equation with Sinusoidal Potentials at Infinity
Year: 2008
Communications in Computational Physics, Vol. 3 (2008), Iss. 3 : pp. 641–658
Abstract
In this paper we study numerical issues related to the Schrödinger equation with sinusoidal potentials at infinity. An exact absorbing boundary condition in a form of Dirichlet-to-Neumann mapping is derived. This boundary condition is based on an analytical expression of the logarithmic derivative of the Floquet solution to Mathieu's equation, which is completely new to the author's knowledge. The implementation of this exact boundary condition is discussed, and a fast evaluation method is used to reduce the computation burden arising from the involved half-order derivative operator. Some numerical tests are given to show the performance of the proposed absorbing boundary conditions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-CiCP-7868
Communications in Computational Physics, Vol. 3 (2008), Iss. 3 : pp. 641–658
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18