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arXiv · 1812.11620

Nonlinear coherent states associated with a measure on the positive real half line

S. Twareque Ali·Zouhaïr Mouayn·Khalid Ahbli
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Abstract

We construct a class of generalized nonlinear coherent states by means of a newly obtained class of 2D complex orthogonal polynomials. The associated coherent states transform is discussed. A polynomials realization of the basis of the quantum states Hilbert space is also obtained. Here, the entire structure owes its existence to a certain measure on the positive real half line, of finite total mass, together with all its moments. We illustrate this construction with the example of the measure $r^βe^{-r}dr$, which leads to a new generalization of the true-polyanalytic Bargmann transform.

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S. Twareque Ali, Zouhaïr Mouayn, Khalid Ahbli. 2018-12-30. Nonlinear coherent states associated with a measure on the positive real half line. https://arxiv.org/abs/1812.11620

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