The Construction of the Dual Family of Gazeau-Klauder Coherent States via Temporally Stable Nonlinear Coherent States

Abstract

Using the {\it analytic representation} of the so-called Gazeau-Klauder coherent states(CSs), we shall demonstrate that how a new class of generalized CSs namely the {\it family of dual states} associated with theses states can be constructed through viewing these states as {\it temporally stable nonlinear CSs}. Also we find that the ladder operators, as well as the displacement type operator corresponding to these two pairs of generalized CSs, may be easily obtained using our formalism, without employing the {\it supersymmetric quantum mechanics}(SUSYQM) techniques. Then, we have applied this method to some physical systems with known spectrum, such as P\"{o}schl-Teller, infinite well, Morse potential and Hydrogen-like spectrum as some quantum mechanical systems. Finally, we propose the generalized form of Gazeau-Klauder CS and the corresponding dual family.