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Title: Polyanalytic relativistic second Bargmann transforms

Abstract

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
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 56; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
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

Citation Formats

Mouayn, Zouhaïr. Polyanalytic relativistic second Bargmann transforms. United States: N. p., 2015. Web. doi:10.1063/1.4919544.
Mouayn, Zouhaïr. Polyanalytic relativistic second Bargmann transforms. United States. doi:10.1063/1.4919544.
Mouayn, Zouhaïr. Fri . "Polyanalytic relativistic second Bargmann transforms". United States. doi:10.1063/1.4919544.
@article{osti_22403148,
title = {Polyanalytic relativistic second Bargmann transforms},
author = {Mouayn, Zouhaïr},
abstractNote = {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.},
doi = {10.1063/1.4919544},
journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 5,
volume = 56,
place = {United States},
year = {2015},
month = {5}
}