A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

AUTOR(ES)

Galetti, Diógenes

FONTE

Brazilian Journal of Physics

DATA DE PUBLICAÇÃO

2003-03

RESUMO

We discuss some results from q-series that can account for the foundations for the introduction of orthogonal polynomials on the circle and on the line, namely the Rogers-Szegö and Stieltjes-Wigert polynomials. These polynomials are explicitly written and their orthogonality is verified. Explicit realizations of the raising and lowering operators for these polynomials are introduced in analogy to those of the Hermite polynomials that are shown to obey the q-commutation relations associated with the q-deformed harmonic oscillator.

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