Spectrum generating algebra and coherent states of the C λ-extended oscillator

Abstract

Cλ-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra, where Cλ is the cyclic group oforder λ, 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 Cλ-extended oscillator. We then construct its coherent states, study their nonclassical properties, and compare the latter with those of standard λ-photon coherent states, which are obtained as a special case. Finally, we briefly review some other types of coherent states associated with the Cλ-extended oscillator.