We propose a generalized su(2) algebra that perfectly describes the discrete energy part of the Morse potential. Then, we examine particular examples and the approach can be applied to any Morse oscillator and to practically any physical system whose spectrum is finite. Further, we construct the Klauder coherent state for Morse potential satisfying the resolution of identity with a positive measure, obtained through the solution of truncated Stieltjes moment problem. The time evolution of the uncertainty relation of the constructed coherent states is analyzed. The uncertainty relation is more localized for small values of radius of convergence.

中文翻译：

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Morse 势相干态的构建：一种类似 su(2) 的方法

我们提出了一个广义的 su(2) 代数，它完美地描述了莫尔斯势的离散能量部分。然后，我们检查特定的例子，该方法可以应用于任何莫尔斯振荡器和几乎任何频谱有限的物理系统。此外，我们为 Morse 势构建了 Klauder 相干态，满足具有正测度的恒等式解析，通过截断 Stieltjes 矩问题的解决方案获得。分析了所构建的相干态不确定性关系的时间演化。对于较小的收敛半径值，不确定性关系更加局部化。