Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics - Marchiolli, M. A. [UNESP]; Ruzzi, M. [UNESP]; Galetti, Diogenes [UNESP] (Iop Publishing Ltd, 2009)
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 detail. 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.