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Journal of Mathematical Physics

Gazeau–Klauder coherent states for trigonometric Rosen–Morse potential

Alireza Chenaghlou, Omid Faizy

Published Feb 1, 2008• 13 citations
Publisher

Abstract

The Gazeau–Klauder coherent states for the trigonometric Rosen–Morse potential are constructed. It is shown that the resolution of unity, temporal stability, and action identity conditions are satisfied for the coherent states. The Mandel parameter is also calculated for the weighting distribution function corresponding to the coherent states.

DOI
10.1063/1.2838316

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The Gazeau–Klauder coherent states for the trigonometric Rosen–Morse potential are constructed. It is shown that the resolution of unity, temporal stability, and action identity conditions are satisfied for the coherent states. The Mandel parameter is also calculated for the weighting distribution function corresponding to the coherent states.
We explicitly construct a Hamiltonian whose exact eigenfunctions are the generalized Laguerre functions. Moreover, we present the related raising and lowering operators. We investigate the corresponding coherent states by adopting the Gazeau–Klauder approach, where resolution of unity and overlapping properties are examined. Coherent states are found to be similar to those found for a particle trapped in a Pöschl–Teller potential of the trigonometric type. Some comparisons with Barut–Girardello and Klauder–Perelomov methods are noted.
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.
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.
The so-called Gazeau–Klauder and Perelomov coherent states are introduced for an arbitrary quantum system. We give also the general framework to construct the generalized intelligent states which minimize the Robertson–Schrödinger uncertainty relation. As illustration, the Pöschl–Teller potentials of trigonometric type will be chosen. We show the advantage of the analytical representations of Gazeau–Klauder and Perelomov coherent states in obtaining the generalized intelligent states in analytical way.