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

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.

9 pages, LaTeX, amssym, talk at the XXIII International Colloquium on Group Theoretical Methods in Physics, Dubna (Russia), 30 July - 5 August, 2000 (without figures)