An Exact Absorbing Boundary Condition for the Schrödinger Equation with Sinusoidal Potentials at Infinity

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

Keywords: