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Complex and real Hermite polynomials and related quantizations

Domenii publicaţii > Fizica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: Nicolae Cotfas , Jean Pierre Gazeau and Katarzyna Górska

Editorial: Professor Murray Batchelor, IOP Science, Journal of Physics A: Mathematical and Theoretical, 43, p.305304, 2010.


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.

Cuvinte cheie: sisteme de stari coerente, quantificari, polinoame Hermite complexe // coherent state quantization, complex Hermite polynomials