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

C. Quesne
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Abstract

$C_λ$-extended oscillator algebras, generalizing the Calogero-Vasiliev algebra, where $C_λ$ is the cyclic group of order $λ$, 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 $C_λ$-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 $C_λ$-extended oscillator.

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C. Quesne. 2000-08-23. Spectrum generating algebra and coherent states of the $C_λ$-extended oscillator. https://arxiv.org/abs/math-ph/0008034

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