Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:math-ph/0312040 · Journal of Mathematical Physics

Generalized coherent and intelligent states for exact solvable quantum systems

A. H. El Kinani, Mohammed Daoud A

Published Feb 1, 2002• 29 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1063/1.1429321

Related papers

Generalized intelligent states for an arbitrary quantum system

A. H. El Kinani, Mohammed Daoud A

Generalized intelligent states (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schrödinger uncertainty relation. The Fock-Bargmann representation is also considered. As a direct illustration of our construction, the Pöschl-Teller potentials of trigonometric type will be chosen. We will show the advantage of the Fock-Bargmann representation in obtaining the generalized intelligent states in an analytical way. Many properties of these states are studied.

arXiv:quant-ph/0311029•Journal of Physics A Mathematical and General•Jun 22, 2001•34 citations

GENERALIZED INTELLIGENT STATES FOR NONLINEAR OSCILLATORS

A. H. EL KINANI, Mohammed Daoud A

The construction of Generalized Intelligent States (GIS) for the x4-anharmonic oscillator is presented. These GIS families are required to minimize the Robertson–Schrödinger uncertainty relation. As a particular case, we will get the so-called Gazeau–Klauder coherent states. The properties of the latters are discussed in detail. Analytical representation is also considered and its advantage is shown in obtaining the GIS in an analytical way. Further extensions are finally proposed.

arXiv:quant-ph/0312121•International Journal of Modern Physics B•Jul 20, 2001•25 citations

COHERENT AND GENERALIZED INTELLIGENT STATES FOR INFINITE SQUARE WELL POTENTIAL AND NONLINEAR OSCILLATORS

A. H. EL KINANI, Mohammed Daoud A

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.1 We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.

arXiv:quant-ph/0312122•International Journal of Modern Physics B•Oct 20, 2002•9 citations

Generalized Intelligent States for Nonlinear Oscillators

A. H. El Kinani, Mohammed Daoud A

The construction of Generalized Intelligent States (GIS) for the $x^4$% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schr\\"odinger uncertainty relation. As a particular case, we will get the so-called Gazeau-Klauder coherent states. The properties of the latters are discussed in detail. Analytical representation is also considered and its advantage is shown in obtaining the GIS in an analytical way. Further extensions are finally proposed.

•Dec 13, 2003•20 citations

Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators

El Hassan El Kinani, Mohammed Daoud A

This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system $[ 1] $. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states \\`{a} la Gazeau-Klauder and those \\`{a} la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways.

•Jan 1, 2001•8 citations

ROBERTSON–SCHRÖDINGER INTELLIGENT STATES FOR TWO-BODY CALOGERO MODEL

Mohammed Daoud A

Using the Gazeau–Klauder and Klauder–Perelomov coherent states, we derive the Robertson–Schrödinger intelligent states for two-body Calogero quantum system.

arXiv:math-ph/0409052•Modern Physics Letters A•Sep 7, 2002•5 citations
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.
Generalized intelligent states (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schrödinger uncertainty relation. The Fock-Bargmann representation is also considered. As a direct illustration of our construction, the Pöschl-Teller potentials of trigonometric type will be chosen. We will show the advantage of the Fock-Bargmann representation in obtaining the generalized intelligent states in an analytical way. Many properties of these states are studied.
The construction of Generalized Intelligent States (GIS) for the x4x^4x4% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schr\\"odinger uncertainty relation. As a particular case, we will get the so-called Gazeau-Klauder coherent states. The properties of the latters are discussed in detail. Analytical representation is also considered and its advantage is shown in obtaining the GIS in an analytical way. Further extensions are finally proposed.