Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass

Abstract

Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU (1, 1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut-Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.

Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations

“…Its main characteristic is that the conventional expression for the kinetic termp 2 2m is not self-adjoint [219,220], so that the Hermiticity of the Hamiltonian is a part of the problem if the mass is not a constant. Nevertheless, different generalized CS have been constructed [249][250][251][252][253][254][255][256][257]. The above is remarkable since well known quantumclassical analogies [38,40,248,[258][259][260] can be exploited to test quantum-theoretical predictions in the laboratory.…”

Supersymmetric approach to coherent states for nonlinear oscillator with spatially dependent effective mass

“…Our appropriate ladder operators act as follows:abadbreakafter−|ψn〉badbreakafter=[n−kn(n+1)]|ψn−1〉1emnewlineidmmlbr0004after;abadbreakafter+|ψn〉goodbreakafter=[(n+1)−k(n+1)(n+2)]|ψn+1〉 where we have set kgoodbreakafter=δ22λ. Note that there are four irreducible representations for the Lie algebra su(1,1) [11]. Strong of the preceding generators, we can determine the coherent states for the nonlinear oscillator with variable mass in the sense of Barut-Girardello.…”

“…For the nonlinear oscillator with variable mass considered, the convergence radius ℓ of the coherent states is defined from Eq. (29) as follows [11]:ℓbadbreakafter=limnfalse→∞⁡ρnngoodbreakafter=limnfalse→∞⁡n!false(badbreakafter−kfalse)ntrue(2badbreakafter−1false/ktrue)nn Computation of ℓ provides us with the following:ℓbadbreakafter=∞ The result given in Eq. (34) shows that Barut-Girardello coherent states for the nonlinear oscillator with variable mass are defined on the entire complex plane.…”

“…In the context of constant mass systems, contributions have been made by many authors. However the generalization of coherent states for variable mass systems has not yet been studied in a significant way [11], [12]. We expect in this work to determine coherent states for a particular variable mass system in the sense of Barut-Girardello and then compare their properties to those already known.…”

“…As a consequence of the many applications in mathematics and physics, the notion of coherent states has been generalized using the algebraic structure of the system [9]. In 1971 Barut and Girardello developed coherent states of noncompact groups [11]. In the context of constant mass systems, contributions have been made by many authors.…”