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Complex and real Hermite polynomials and related quantizations
Cotfas N., Gazeau J.-P., Górska K.
Journal of Physics A: Mathematical and Theoretical 43 (2010) 305304 - http://hal.archives-ouvertes.fr/hal-00739323
Physique/Physique mathématique
Mathématiques/Physique mathématique
Complex and real Hermite polynomials and related quantizations
N. Cotfas1, J.-P. Gazeau2, K. Górska
1 :  Faculty of Physics
University of Bucharest
Bucharest
Roumanie
2 :  APC - UMR 7164 - AstroParticule et Cosmologie
http://www.apc.univ-paris7.fr/
CNRS : UMR7164 – IN2P3 – Observatoire de Paris – Université Paris VII - Paris Diderot – CEA : DSM/IRFU
APC - UMR 7164, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, case postale 7020, F-75205 Paris Cedex 13
France
APC - THEORIE
It is known that the anti-Wick (or standard coherent state) quantization of the complex plane produces both canonical commutation rule and quantum spectrum of the harmonic oscillator (up to the addition of a constant). In this work, we show that these two issues are not necessarily coupled: there exists a family of separable Hilbert spaces, including the usual Fock-Bargmann space, and in each element in this family there exists an overcomplete set of unit-norm states resolving the unity. With the exception of the Fock-Bargmann case, they all produce non-canonical commutation relation whereas the quantum spectrum of the harmonic oscillator remains the same up to the addition of a constant. The statistical aspects of these non-equivalent coherent state quantizations are investigated. We also explore the localization aspects in the real line yielded by similar quantizations based on real Hermite polynomials.
Anglais

Journal of Physics A: Mathematical and Theoretical
Publisher Institute of Physics: Hybrid Open Access
ISSN 1751-8113 (eISSN : 1751-8121)
internationale
Articles dans des revues avec comité de lecture
07/2010
43
305304