Volume 3, Issue 3
An Exact Absorbing Boundary Condition for the Schrödinger Equation with Sinusoidal Potentials at Infinity

Chunxiong Zheng

DOI:

Commun. Comput. Phys., 3 (2008), pp. 641-658.

Published online: 2008-03

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  • 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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@Article{CiCP-3-641, author = {}, title = {An Exact Absorbing Boundary Condition for the Schrödinger Equation with Sinusoidal Potentials at Infinity}, journal = {Communications in Computational Physics}, year = {2008}, volume = {3}, number = {3}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7868.html} }
TY - JOUR T1 - An Exact Absorbing Boundary Condition for the Schrödinger Equation with Sinusoidal Potentials at Infinity JO - Communications in Computational Physics VL - 3 SP - 641 EP - 658 PY - 2008 DA - 2008/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7868.html KW - AB -

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.

Chunxiong Zheng. (2020). An Exact Absorbing Boundary Condition for the Schrödinger Equation with Sinusoidal Potentials at Infinity. Communications in Computational Physics. 3 (3). 641-658. doi:
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