We introduce a generalization structure of the su(1,1) algebra which depends on a function of one generator of the algebra, f(H). Following the same ideas developed to the generalized Heisenberg algebra (GHA) and to the generalized su(2), we show that a symmetry is present in the sequence of eigenvalues of one generator of the algebra. Then, we construct the Barut-Girardello coherent states associated with the generalized su(1,1) algebra for a particle in a Poschl-Teller potential. Furthermore, we compare the time evolution of the uncertainty relation of the constructed coherent states with that of GHA coherent states. The generalized su(1,1) coherent states are very localized.

中文翻译：

---

广义 su(1,1) 代数和 Pöschl-Teller 势的非线性相干态的构造

我们介绍了 su(1,1) 代数的泛化结构，它依赖于代数的一个生成器 f(H) 的函数。遵循对广义海森堡代数 (GHA) 和广义 su(2) 发展的相同思想，我们表明在代数的一个生成器的特征值序列中存在对称性。然后，我们构造与 Poschl-Teller 势中粒子的广义 su(1,1) 代数相关的 Barut-Girardello 相干态。此外，我们将构建的相干态的不确定性关系与 GHA 相干态的不确定性关系的时间演化进行了比较。广义 su(1,1) 相干状态非常局部化。