Faculty of Physics - University of Bucharest

UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS

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2024-11-22 2:35

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Conference: Bucharest University Faculty of Physics 2010 Meeting

Section: Theoretical Physics and Applied Mathematics

Title:

Complex and real Hermite polynomials and related quantizations

Authors:

Nicolae Cotfas

Affiliation:

Physics Department, University of Bucharest

E-mail

ncotfas@yahoo.com

Keywords:

Hermite polynomials, complex Hermite polynomials, coherent state quantization, Fock-Bargmann space

Abstract:

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). We show that these two issues are not necessarily coupled: there exists a family of separable Hilbert spaces, including the ``canonical`` 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 states quantizations are investigated. We also explore the localization aspects in the real line yielded by similar quantizations based on real Hermite polynomials.