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

Abstract

We construct a new class of coherent states labeled by points z of the complex plane and depending on three numbers (γ, ν) and ε > 0 by replacing the coefficients z n / √ n! of the canonical coherent states by Laguerre polynomials. These states are superpositions of eigenstates of the symmetric Pöschl-Teller oscillator and they solve the identity of the states Hilbert space at the limit ε → 0 + . Their wavefunctions are obtained in a closed form for a special case of parameters (γ, ν). We discuss their associated coherent states transform which leads to an integral representation of Hankel type for Laguerre functions.