This paper describes the calculation of the stationary scattering matrix and its derivatives for Euclidean waveguides. This is an adaptation and extension to a procedure developed by Levitin and Strohmaier which was used to compute the stationary scattering matrix \cite{alexnew}. On Euclidean waveguides, the scattering matrix can be meromorphically continued from the complex plane to a Riemann surface with a countably infinite number of sheets. We describe in detail how we have dealt with this. In addition, our algorithm is also able to calculate arbitrarily high derivatives. In the final section, we will present the results of some numerical calculations obtained using this method.

翻译：本文描述固定散射矩阵的计算及其在欧几里得波导的衍生物。 这是对利维廷和斯特罗哈马耶开发的程序的调整和扩展, 用于计算固定散射矩阵 \ cite{alexnew} 。 在欧几里德波导 上, 散射矩阵可以从复杂的平面到里曼表面, 以可计算到无限的平面。 我们详细描述我们是如何处理这个问题的。 此外, 我们的算法还可以计算任意高的衍生物。 在最后一节, 我们将介绍使用这种方法得出的一些数字计算结果 。