An Exact Absorbing Boundary Condition for the Schrödinger Equation with Sinusoidal Potentials at Infinity (Communications in Computational Physics, 2008)
In this paper we study numerical issues related to the Schrödinger equationwith sinusoidal potentials at infinity. An exact absorbing boundary condition in a formof Dirichlet-to-Neumann mapping is derived. This boundary condition is based on ananalytical expression of the logarithmic derivative of the Floquet solution to Mathieu'sequation, which is completely new to the author's knowledge. The implementationof this exact boundary condition is discussed, and a fast evaluation method is used toreduce the computation burden arising from the involved half-order derivative operator. Some numerical tests are given to show the performance of the proposed absorbingboundary conditions.