Generalized su(1,1) algebra and the construction of nonlinear coherent states for Pöschl-Teller potential

Phase-space behavior of physical nonlinear coherent states

“…The su(1, 1) algebra can also be generalized [28] similarly to the Heisenberg algebra and the su(2) algebra [29,30]. Let † A and A be two operators which together with the dimensionless Hamiltonian H obey the following relations…”

“…Let us now construct the generalized su(1, 1) nonlinear coherent states [28]. Let | ñ z be an eigenvector of the generalized su(1, 1) algebra annihilation operator A with eigenvalue z, | | ñ = ñ A z z z .…”

“…, then another kind of nonlinear coherent states can be constructed in addition to the GHA coherent states [25,28].…”

“…For simplicity, from now on we will consider that ν=0 since the spectrum as well as the eigenfunctions of the Pöschl-Teller potential for this particular case are similar to those of the square-well potential [28]. Therefore, the generalized su(1, 1) nonlinear coherent state can be written as [28]…”

“…The vector | ñ z given in (53) satisfies the conditions (32) and(33). Meanwhile, the condition (34) is satisfied if there exists a function w(x) such that To determine w(x), we use the convolution of the Mellin transform[28,[34][35][36]. If…”