Gazeau–Klauder coherent states examined from the viewpoint of diagonal ordering operation technique

Popov, Dušan; Negrea, Romeo; Popov, Miodrag

doi:10.1088/1674-1056/25/7/070301

Cited by 4 publications

(3 citation statements)

References 18 publications

(30 reference statements)

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“…The DOOT can be applied also in order to construct the CSs in the Gazeau-Klauder manner [24]. Moreover, by the help of DOOT, we have showed that the coherent states for the continuous spectrum can be regarded as the limiting case of hypergeometric Barut-Girardello coherent states (GH-BG-CSs) [25].…”

Section: Some Applicationsmentioning

confidence: 99%

Coherent States of Systems with Non-Equidistant Energy Levels

Popov¹

2017

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Abstract. In the paper we have built and examined the properties of quantum systems with nonequidistant energy levels from a point of view of a new introduced approach -the diagonal operator ordering technique (DOOT). In this frame, we examine also the properties of mixed states described by a canonical density operator. We particularize the obtained results for some particular cases (the system with Hamiltonian whose eigenfunctions are the generalized Laguerre functions, as well as the Pöschl-Teller like potentials, and the infinite quantum well).Keywords: Coherent states, operator ordering, density operator, energy spectra. IntroductionIt is well-known that a most popular and also most applicable quantum model is the one-dimensional harmonic oscillator (HO-1D). An important feature of HO-1D is its equidistant energy levels, which ease the various mathematical characterizations of their different physical properties, especially in the case of mixed (thermal) states. On the other hand, among the quantum systems allowing an exact solution of the nonrelativistic stationary Schrödinger equation, a special place is occupied by the systems with nonequidistant energy levels. Generally, the appearance of non-equidistant energy levels is determined by the anharmonic character of the potential. Such systems are, e.g. the infinitely deep square-well potential, the potential whose eigenfunctions are the generalized Laguerre functions, the Pöschl-Teller like potential, the Morse potential and so on (see, [1], and references therein). In this book were examined the coherent states (CSs) of these potentials in the frame of factorization method. Also, in [2] were built the CSs for systems related to the generalized Laguerre functions. These CSs are known in the quantum optical literature as belonging to the nonlinear coherent states (NCSs) which generally is an overcomplete set of vectors in Hilbert space. On the other hand, the NCSs can be regarded as particular cases of more general CSs, namely the so called generalized hypergeometric coherent states (GH-CSs) whose appellation becomes from their normalization function which is given by a generalized hypergeometric function [3], [4]. Let us denote by, and φ π   ∈   0, 2 , the continuous parameter which labels the CSs and run over a complex domain. Moreover, any set of CSs must fulfill some conditions summarized by Klauder (called "the Klauder's prescriptions"): continuity in the complex label z , non-orthogonality, but normalization, unity operator resolution with positive defined integration measure, temporal stability and action identity [5].In different calculations involving the CSs it is necessary to use some rules for the operator ordering. A useful and practical technique applicable to the canonical CSs related with the HO-1D, namely, the integration within an ordered product (IWOP) technique, was elaborated by H. -Y. Fan (see, e.g. [6] and references therein). Generally, for any pair of lowering − L and raising + L operators, which generate the GH-CSs, previously ...

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Section: Some Applicationsmentioning

confidence: 99%

Coherent States of Systems with Non-Equidistant Energy Levels

Popov¹

2017

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“…In a series of previous works, we have generalized the IWOP technique and applied it to the pair of creation 􏽢 E + , and annihilation 􏽢 E − , operators associated with any quantum system, linear or nonlinear. us, it was born the diagonal operator ordering technique (DOOT) was born, with which we obtained a series of useful results [17][18][19]. An additional result of using DOOT appears in this paper: we obtain a series of new integration relations involving Meijer's G m,n p,q (|z| 2 | .…”

Section: Introductionmentioning

confidence: 97%

Some Integrals Involving Meijer’s and Hypergeometric Functions Using the Coherent State Technique

Popov

Negrea

2022

Mathematical Problems in Engineering

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In this paper, we have examined a particular case of coherent states, defined so that their structure constants depend only on the products of the energy eigenvalues of the examined systems. In this manner, we have built all three kinds of coherent states (Barut–Girardello, Klauder–Perelomov, and Gazeau–Klauder). From the equation of the unitary operator decomposition, we have highlighted and used a so-called fundamental integral, to obtain some new integrals involving Meijer’s and hypergeometric functions. All calculations are made using the properties of the diagonal operator ordering technique. This is implicitly proved that the coherent state technique can be useful not only in different branches of physics (quantum mechanics, quantum optics, quantum information theory, and so on) but also in the deduction of new integrals involving generalized Meijer’s and hypergeometric functions. This approach can be considered as suitable “feedback” from physics to mathematics.

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“…In 1999, Gazeau and Klauder (GK) [18] proposed new coherent states for semibounded Hamiltonian operators having either a discrete or continuous spectrum. These states, which have been constructed for a large variety of quantum systems [19][20][21][22][23][24][25][26][27], also satisfy the Klauderʼs minimum requirements.…”

Section: Introductionmentioning

confidence: 97%

Gazeau-Klauder coherent states in position-deformed Heisenberg algebra

Lawson

Osei

2022

J. Phys. Commun.

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In this paper, we present coherent states à la Gazeau-Klauder for a free particle in square well potential within position-deformed Heisenberg algebra. These states satisfy the Klauder's mathematical requirement to build coherent states. Some statistical properties such as the probability distribution, the intensity correlation function and the Mandel parameter are calculated and analyzed. We find that these states are sub-Poissonian in nature. We also construct for these coherent states, the even cat states and we evaluate its Wigner function which analyses the quasiprobability distribution of these states. We graphically demonstrate that these states exhibit nonclassical behavior.

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Gazeau–Klauder coherent states examined from the viewpoint of diagonal ordering operation technique

Cited by 4 publications

References 18 publications

Coherent States of Systems with Non-Equidistant Energy Levels

Coherent States of Systems with Non-Equidistant Energy Levels

Some Integrals Involving Meijer’s and Hypergeometric Functions Using the Coherent State Technique

Gazeau-Klauder coherent states in position-deformed Heisenberg algebra

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