Fast evaluation of nonreflecting boundary conditions for the Schrödinger equation in one dimension

✍ Scribed by Shidong Jiang; L Greengard

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 722 KB
• Volume: 47
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(04)90079-x

✦ Synopsis

We

present a fast algorithm for the evaluation of the exact nonreflecting boundary conditions for the SchrSdinger equation in one dimension. The exact nonrefleeting boundary condition contains a nonloeal term which is a convolution integral in time, with a kernel proportional to 1/v~.

The key observation is that this integral can be split into two parts: a local part and a history part, each of which allows for separate treatment. The local part is computed by a quadrature suited for square-root singularities. For the history part, we approximate the convolution kernel uniformly by a sum of exponentials. The integral can then be evaluated reeursively. As a result, the computation of the nonrefleeting boundary conditions is both accurate and efficient. (~) 2004 Elsevier Ltd. All rights reserved.