New coherent states with Laguerre polynomials coefficients for the symmetric Pöschl–Teller oscillator

We construct new coherent states labeled by points z of the complex plane and depending on three parameters $\gamma ,\nu$ and $\epsilon >0$ by replacing the coefficients $z^n/\sqrt{n!}$ of the canonical coherent states by Laguerre polynomials with an order depending on γ. These coherent states are superpositions of eigenstates of the Hamiltonian with a symmetric Pöschl–Teller potential indexed by ν, which solve an ϵ-identity operator while the resolution of the identity of the states Hilbert space is acheived at the limit $\epsilon \to 0^{+}.$ We obtain their wave functions in a closed form for a special case of parameters γ and ν. We also discuss their associated coherent states transform which leads to an integral representation of Hankel type for Laguerre functions. (paper)