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Etats cohérents et intelligents généralisés pour des systèmes quantiques exactement solubles

A. H. El Kinani

Published Feb 1, 2006• 0 citations
OpenAlex

Abstract

In this Letter we present a scheme for constructing the coherent states of Klauder–Perelomov’s type for a particle which is trapped in Poschl–Teller potentials.  2001 Elsevier Science B.V. All rights reserved.

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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.
This article is a direct illustration of a construction of coherent states which has been recently proposed by two of us (JPG and JK). We have chosen the example of a particle trapped in an infinite square-well and also in Pöschl–Teller potentials of the trigonometric type. In the construction of the corresponding coherent states, we take advantage of the simplicity of the solutions, which ultimately stems from the fact they share a common SU(1,1) symmetry à la Barut-Girardello. Many properties of these states are then studied, both from mathematical and from physical points of view.
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.