Non-relativistic quantum particles bounded to a curve in [Formula: see text] by attractive contact [Formula: see text]-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous spectrum, with possible embedded eigenvalues. The existence of the wave operators is proved for the mentioned energy interval using the Hamiltonians with the interaction supported by the straight lines as the free ones. Their completeness is not proved. The curve is assumed [Formula: see text]-smooth, non-intersecting, unbounded, asymptotically approaching two different half-lines (non-parallel or parallel but excluding the “U-case”). Physically, the system can be considered as a model of long nanostructural channel.

中文翻译：

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以无限平面曲线为界的粒子散射

非相对论量子粒子通过吸引接触[公式：见文本]-相互作用限制在 [公式：见文本] 中的曲线上。横向束缚态的能量与零之间的区间被证明属于绝对连续谱，具有可能的嵌入特征值。使用由直线支持的相互作用作为自由相互作用的哈密顿量证明了上述能量区间的波算子的存在。它们的完整性没有得到证明。假定曲线[公式：见正文]-平滑、不相交、无界、渐近地接近两条不同的半线（不平行或平行，但不包括“U 型”）。在物理上，该系统可以被认为是长纳米结构通道的模型。