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Modern Physics Letters A

KLAUDER–PERELOMOV AND GAZEAU–KLAUDER COHERENT STATES FOR SOME SHAPE INVARIANT POTENTIALS

Alireza Chenaghlou, Hossein Fakhri

Published Aug 30, 2002• 27 citations
Publisher

Abstract

Firstly, the solvability of some quantum models like Eckart and Rosen–Morse II are explained on the basis of the shape invariance theory. Then, two generalized types of the Klauder–Perelomov and Gazeau–Klauder coherent states are calculated for the models. By means of calculating the Mandel parameter, it is shown that the weight distribution function of the first type coherent states obeys the Poissonian and super-Poissonian statistics, however, the weight distribution function of the second type coherent states obeys the Poissonian and sub-Poissonian statistics.

DOI
10.1142/s0217732302008095

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Firstly, the solvability of some quantum models like Eckart and Rosen–Morse II are explained on the basis of the shape invariance theory. Then, two generalized types of the Klauder–Perelomov and Gazeau–Klauder coherent states are calculated for the models. By means of calculating the Mandel parameter, it is shown that the weight distribution function of the first type coherent states obeys the Poissonian and super-Poissonian statistics, however, the weight distribution function of the second type coherent states obeys the Poissonian and sub-Poissonian statistics.
Using the Kinani-Daoud method we have constructed the Gazeau-Klauder(GK) and KlauderPerelomov(KP) coherent states for the anharmonic oscillator. It is shown that the two types of coherent states have totally different forms in their expressions. We have also discussed the resolution of unity of the two coherent states and the Hilbert space of each state. The study of Mandel Q pa rameter of the states shows that GK coherent state coincides with the sub-Poissonian and KP coherent state coincides with the super-Poissonian statistical distributions.
Generalized coherent states based on Gazeau-Klauder formalism are developed for one-dimensional power-law potentials and their quantum statistical characteristics, together with generalized Heisenberg algebra coherent states, are reported. We show that these states exhibit super-Poissonian, Poissonian, or sub-Poissonian distributions as a function of the power-law exponent. The analytical results are supported by numerical calculations. In addition, we explain possible sources of errors in numerical analysis.
Abstract 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.
We develop generalized coherent states based on the Gazeau–Klauder formalism for a particle with position-dependent mass trapped in an infinite square well. We study the quantum statistical properties of these states by means of the Mandel parameter and the second-order correlation function. Our analysis reveals that the constructed coherent states exhibit sub-Poissonian statistics. Moreover, theoretical investigations of wave packet revivals and fractional revivals for the pertaining system have been performed by means of the autocorrelation function and temporal evolution of probability density.