New coherent states with Laguerre polynomials coefficients for the symmetric Poschl-Teller oscillator

TL;DR

This paper introduces a new class of coherent states for the symmetric Poschl-Teller oscillator, using Laguerre polynomial coefficients, which form a complete basis in the limit and have a specific integral transform representation.

Contribution

It constructs novel coherent states with Laguerre polynomial coefficients for the symmetric Poschl-Teller oscillator, including explicit wavefunctions and a related integral transform.

Findings

States form a complete basis as epsilon approaches zero

Wavefunctions are explicitly derived for specific parameters

Coherent states transform yields a Hankel-type integral representation

Abstract

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