We make a relativistic extension of the one-dimensional J -matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential functions (not necessarily analytic like a square well) such that they are well represented by their matrix elements in a finite subset of a square integrable basis set. This set is chosen to support a tridiagonal symmetric matrix representation for the free Dirac operator. We derive the transmission and reflection coefficients. This work will be followed by another where we apply the theory to obtain scattering information for different potential coupling modes including those with evidence of Klein tunneling and of supercritical resonances.

中文翻译：

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1 + 1时空散射的相对论J矩阵方法I.理论*

我们对散射的一维J矩阵方法进行了相对论的扩展。相对论势矩阵是矢量，标量和伪标量分量的组合。这些是非奇异的短距离势函数（不一定像正方形阱那样进行分析），因此它们可以由正方形可积基础集的有限子集中的矩阵元素很好地表示。选择该集合以支持自由Dirac算子的三对角对称矩阵表示。我们得出透射系数和反射系数。这项工作之后将进行另一项研究，我们将应用该理论来获得不同潜在耦合模式的散射信息，包括具有Klein隧穿和超临界共振证据的模式。