Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

Details Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

2009-03-24

arxiv.org/abs/0903.4059v2

Physics

Quantum Physics

Sections 3 and 5 modified; Section 6 (Applications) included; References added; Submitted to Journal of Physics A: Mathematica

Scientific paper

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.

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