2012/12/25 by Zouhaı̈r Mouayn, Mouayn, Zouhair
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1212.5977
openalex publication_date 2012/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct coherent states through special superpositions of photon number states of the relativistic isotonic oscillator. In each superposition the coefficients are chosen to be L 2 eingenfunctions of a sigma weight Maass Laplacian on the Poincare disk, which are associated with discrete eigenvalues. For each nonzero m the associated coherent states transform constitutes the m true polyanalytic extension of a relativistic version of the second Bargmann transform, whose integral kernel is expressed in terms of a special Appel Kampe de Feriet hypergeometric function. The obtained results could be used to extend the known semi classical analysis of quantum dynamics of the relativistic isotonic oscillator.