✍ Scribed by C. Quesne
No coin nor oath required. For personal study only.
Two new types of coherent states associated with the C λ -extended oscillator, where C λ is the cyclic group of order λ, are introduced. The first ones include as special cases both the Barut-Girardello and the Perelomov su(1,1) coherent states for λ = 2, as well as the annihilation-operator coherent states of the C λ -extended oscillator spectrum-generating algebra for higher λ values. The second ones, which are eigenstates of the C λ -extended oscillator annihilation operator, extend to higher λ values the paraboson coherent states, to which they reduce for λ = 2. All these states satisfy a unity resolution relation in the C λ -extended oscillator Fock space (or in some subspace thereof). They give rise to Bargmann representations of the latter, wherein the generators of the C λ -extended oscillator algebra are realized as differential-operator-valued matrices (or differential operators). The statistical and squeezing properties of the new coherent states are investigated over a wide range of parameters and some interesting nonclassical features are exhibited.
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