Polyanalytic relativistic second Bargmann transforms

Journal Article · Fri May 15 00:00:00 EDT 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4919544· OSTI ID:22403148

Mouayn, Zouhaïr ^[1]

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1. Faculty of Sciences and Technics (M’Ghila), P.O. Box 523, Béni Mellal (Morocco)

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.

• OSTI ID: 22403148
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNIHILATION OPERATORS
EIGENFUNCTIONS
EIGENSTATES
EIGENVALUES
HYPERGEOMETRIC FUNCTIONS
KERNELS
LAPLACIAN
OSCILLATORS