The Wigner function associated to the Rogers-Szego polynomials

Details The Wigner function associated to the Rogers-Szego polynomials The Wigner function associated to the Rogers-Szego polynomials

2004-04-12

arxiv.org/abs/quant-ph/0404074v2

Physics

Quantum Physics

12 pages, 2 (mathemathica) figures

Scientific paper

10.1088/0305-4470/37/50/L01

We show here that besides the well known Hermite polynomials, the q-deformed harmonic oscillator algebra admits another function space associated to a particular family of q-polynomials, namely the Rogers-Szego polynomials. Their main properties are presented, the associated Wigner function is calculated and its properties are discussed. It is shown that the angle probability density obtained from the Wigner function is a well-behaved function defined in the interval [-Pi,Pi), while the action probability only assumes integer values greater or equal than zero. It is emphasized the fact that the width of the angle probability density is governed by the free parameter q characterizing the polynomial.

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