We analyze the structure of the scattering matrix, S(k), for the one-dimensional Morse potential. We show that, in addition to a finite number of bound state poles and an infinite number of antibound poles, there exist infinite redundant poles, on the positive imaginary axis, which do not correspond to either of the other types. We explain in detail the role of these redundant poles, in particular when they coincide with the bound poles. This can be solved analytically and exactly. In addition, we obtain wave functions for all these poles and ladder operators connecting them.

中文翻译：

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一维莫尔斯电势的S矩阵的冗余极点

我们分析了一维莫尔斯电势的散射矩阵S（k）的结构。我们证明，除了有限数量的束缚态极点和无限数量的反束缚极点之外，在正虚轴上还存在无限的冗余极点，它们与其他任何一种都不对应。我们将详细解释这些冗余极点的作用，尤其是当它们与绑定极点重合时。这可以通过解析准确地解决。另外，我们获得所有这些极点和连接它们的阶梯算子的波动函数。