We present exact solutions for the Lippmann–Schwinger equation in two dimensions for circular boundary walls in three cases: (i) a finite number N of concentric barriers; (ii) a single barrier with Dirac delta derivatives, in the sense of distribution theory, namely, angular, normal, and along the curve; and (iii) a single barrier with an arbitrary distribution. As an application of this last result, we obtain conditions that must be fulfilled in order for the barrier to become invisible.

中文翻译：

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二维和不可见条件下Lippmann-Schwinger方程的精确解

我们提出了在两个维度上为圆形边界壁李普曼-薛定谔方程的精确解在三种情况：（ⅰ）的有限数目Ñ的同心障碍; （ii）从分布理论的角度来看，具有狄拉克三角洲导数的单个障碍，即角度，法线和沿曲线；（iii）具有任意分布的单个障碍。作为最后结果的应用，我们获得了必须满足的条件才能使障碍变得不可见。