Generalized coherent and intelligent states for exact solvable quantum systems

TL;DR

This paper introduces generalized coherent and intelligent states for exactly solvable quantum systems, providing a unified framework and analytical methods, exemplified by P"oschl-Teller potentials.

Contribution

It develops a general framework for constructing generalized intelligent states that minimize uncertainty relations for arbitrary quantum systems.

Findings

Analytical representations of coherent states facilitate the construction of intelligent states.

Application to P"oschl-Teller potentials demonstrates the framework's effectiveness.

Unified approach enhances understanding of quantum state properties.

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-Schr\"odinger uncertainty relation. As illustration, the P\"oschl-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.