Spectrum generating algebra and coherent states of the $C_{\lambda}$-extended oscillator

TL;DR

This paper explores the algebraic structure and coherent states of the $C_{inite}$-extended oscillator, revealing its spectrum generating algebra, constructing its coherent states, and analyzing their nonclassical properties.

Contribution

It determines the spectrum generating algebra and constructs coherent states for the $C_{inite}$-extended oscillator, extending understanding of its algebraic and quantum properties.

Findings

Spectrum generating algebra of the $C_{inite}$-extended oscillator identified.

Constructed and analyzed nonclassical properties of the oscillator's coherent states.

Compared these states with standard $inite$-photon coherent states.

Abstract

$C_{\lambda}$-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra, where $C_{\lambda}$ is the cyclic group of order $\lambda$, have recently proved very useful in the context of supersymmetric quantum mechanics and some of its variants. Here we determine the spectrum generating algebra of the $C_{\lambda}$-extended oscillator. We then construct its coherent states, study their nonclassical properties, and compare the latter with those of standard $\lambda$-photon coherent states, which are obtained as a special case. Finally, we briefly review some other types of coherent states associated with the $C_{\lambda}$-extended oscillator.