Spectrum generating algebra and coherent states of the $C_λ$-extended oscillator

Details Spectrum generating algebra and coherent states of the $C_λ$-extended oscillator Spectrum generating algebra and coherent states of the $C_λ$-extended oscillator

2000-08-23

arxiv.org/abs/math-ph/0008034v1

Phys. At. Nucl. 68 (2005) 1941-1946

Physics

Mathematical Physics

9 pages, LaTeX, amssym, talk at the XXIII International Colloquium on Group Theoretical Methods in Physics, Dubna (Russia), 30

Scientific paper

$C_{\lambda}$-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.

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