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

2018/12/30 by S. Twareque Ali, Ali, S. Twareque, Zouhaı̈r Mouayn +3
Physics and Astronomy · Mathematics · #Quantum Mechanics and Non-Hermitian Physics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1812.11620

Abstract

We construct a class of generalized nonlinear coherent states by means of a\nnewly obtained class of 2D complex orthogonal polynomials. The associated\ncoherent states transform is discussed. A polynomials realization of the basis\nof the quantum states Hilbert space is also obtained. Here, the entire\nstructure owes its existence to a certain measure on the positive real half\nline, of finite total mass, together with all its moments. We illustrate this\nconstruction with the example of the measure r^\β e^-rdr, which leads to\na new generalization of the true-polyanalytic Bargmann transform.\n

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