On The Construction of Generalized Coherent States for Generalized Harmonic Oscillators

TL;DR

This paper introduces a dynamical algebra that encompasses various deformed harmonic oscillator algebras, develops a method for constructing coherent states for these algebras, and applies it to a specific case.

Contribution

It presents a new algebraic framework and a general method for constructing coherent states for generalized harmonic oscillators.

Findings

Introduces the algebra ${\

Develops a general construction method for coherent states.

Applies the method to a specific algebra case.

Abstract

A dynamical algebra ${\cal A}_q$, englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the type ${\cal A}_q$ is discussed. The construction following this method is carried out for the special case.