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Title: Polyanalytic relativistic second Bargmann transforms

We construct coherent states through special superpositions of eigenstates of the relativistic isotonic oscillator. In each superposition, the coefficients are chosen to be L{sup 2}-eigenfunctions of a σ-weight Maass Laplacian on the Poincaré disk, which are associated with the eigenvalue 4m(σ−1−m), m∈Z{sub +}∩[0,(σ−1)/2]. 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-Kampé de Fériet’s hypergeometric function. The obtained results could be used to extend the known semi-classical analysis of quantum dynamics of the relativistic isotonic oscillator.
Authors:
 [1]
  1. Faculty of Sciences and Technics (M’Ghila), P.O. Box 523, Béni Mellal (Morocco)
Publication Date:
OSTI Identifier:
22403148
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; EIGENFUNCTIONS; EIGENSTATES; EIGENVALUES; HYPERGEOMETRIC FUNCTIONS; KERNELS; LAPLACIAN; OSCILLATORS