In this paper, we construct the generalized su(1, 1) nonlinear coherent states for particular physical systems. We study the behavior of the Wigner function for coherent states built from differential operators that satisfy either a generalized Heisenberg algebra or a generalized su(1, 1) nonlinear algebra. The systems studied are the harmonic oscillator and those ones associated with Pöschl-Teller potentials. The results show that the Wigner function for the associated nonlinear coherent states is positive for small values of their convergence radius. Furthermore, the Wigner function for these coherent states depends on the corresponding algebraic structure.

中文翻译：

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物理非线性相干态的相空间行为

在本文中，我们构造了特定物理系统的广义su（1，1）非线性相干态。我们研究了由满足广义Heisenberg代数或广义su（1，1）非线性代数的微分算符构建的相干态的Wigner函数的行为。所研究的系统是谐波振荡器以及那些与Pöschl-Teller电位相关的系统。结果表明，相关联的非线性相干状态的Wigner函数对于较小的会聚半径值是正的。此外，这些相干态的维格纳函数取决于相应的代数结构。