dorsal/arxiv
View SchemaThe Wigner function associated to the Rogers-Szego polynomials
| Authors | D. Galetti, S. S. Mizrahi, M. Ruzzi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404074 |
| URL | https://arxiv.org/abs/quant-ph/0404074 |
| DOI | 10.1088/0305-4470/37/50/L01 |
Abstract
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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"abstract": "We show here that besides the well known Hermite polynomials, the q-deformed\nharmonic oscillator algebra admits another function space associated to a\nparticular family of q-polynomials, namely the Rogers-Szego polynomials. Their\nmain properties are presented, the associated Wigner function is calculated and\nits properties are discussed. It is shown that the angle probability density\nobtained from the Wigner function is a well-behaved function defined in the\ninterval [-Pi,Pi), while the action probability only assumes integer values\ngreater or equal than zero. It is emphasized the fact that the width of the\nangle probability density is governed by the free parameter q characterizing\nthe polynomial.",
"arxiv_id": "quant-ph/0404074",
"authors": [
"D. Galetti",
"S. S. Mizrahi",
"M. Ruzzi"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/37/50/L01",
"title": "The Wigner function associated to the Rogers-Szego polynomials",
"url": "https://arxiv.org/abs/quant-ph/0404074"
},
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