Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics
Abstract
By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in details. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.
Keywords
Cite
@article{arxiv.0903.4059,
title = {Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics},
author = {M A Marchiolli and M Ruzzi and D Galetti},
journal= {arXiv preprint arXiv:0903.4059},
year = {2009}
}
Comments
Sections 3 and 5 modified; Section 6 (Applications) included; References added; Submitted to Journal of Physics A: Mathematical and Theoretical