Special Deformed Exponential Functions Leading to More Consistent Klauder's Coherent States

TL;DR

This paper introduces a new class of deformed exponential functions to construct deformed oscillators and Klauder's Coherent States, providing a unified framework that generalizes traditional exponential functions and ensures convergence within a specific radius.

Contribution

The paper presents a novel approach to constructing deformed oscillators using specially designed deformed exponential functions, extending the theory of Klauder's Coherent States.

Findings

Deformed exponential functions converge to ordinary exponentials as deformation parameters approach one.

Explicit forms of Klauder's Coherent States are derived using these deformed functions.

The convergence radius of the quantum series is calculated and established.

Abstract

We give a general approach for the construction of deformed oscillators. These ones could be seen as describing deformed bosons. Basing on new definitions of certain quantum series, we demonstrate that they are nothing but the ordinary exponential functions in the limit when the deformation parameters goes to one. We also prove that these series converge to a complex function, in a given convergence radius that we calculate. Klauder's Coherent States are explicitly found through these functions that we design by deformed exponential functions