@Article{CiCP-3-3,
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 = {<p style="text-align: justify;">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&#39;s
equation, which is completely new to the author&#39;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.</p>},
issn = {1991-7120},
doi = {https://doi.org/2008-CiCP-7868},
url = {https://global-sci.com/article/81215/an-exact-absorbing-boundary-condition-for-the-schrodinger-equation-with-sinusoidal-potentials-at-infinity}
}