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| Titre : |
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Complex and real Hermite polynomials and related quantizations |
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| Auteur(s) : |
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N. Cotfas1, J.-P. Gazeau2, K. Górska |
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| Laboratoire : |
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| équipe(s) de recherche : |
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APC - THEORIE |
| Résumé : |
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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. |
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Langue du texte
intégral : |
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Anglais |
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| Journal : |
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| Journal of Physics A: Mathematical and Theoretical |
| Publisher |
Institute of Physics: Hybrid Open Access |
| ISSN |
1751-8113 (eISSN : 1751-8121) |
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| Audience : |
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internationale |
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| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Date de publication : |
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07/2010 |
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| Volume : |
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43 |
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| Page, identifiant, ... : |
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305304 |
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