Phase-space behavior of physical nonlinear coherent states

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.