The Wigner distribution function for the one-dimensional parabose oscillator

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dc.creatorJafarov, E. I.
dc.creatorLievens, S.
dc.creatorVan der Jeugt, J.
dc.date2008-01-29
dc.date2008-06-27
dc.date.accessioned2026-07-07T09:46:47Z
dc.date.available2026-07-07T09:46:47Z
dc.descriptionIn the beginning of the 1950's, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the so-called Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. In this article, we consider which definition for such distribution function could be used in the case of non-canonical quantum mechanics. We then explicitly compute two different expressions for this distribution function for the case of the parabose oscillator. Both expressions turn out to be multiple sums involving (generalized) Laguerre polynomials. Plots then show that the Wigner distribution function for the ground state of the parabose oscillator is similar in behaviour to the Wigner distribution function of the first excited state of the canonical quantum oscillator.
dc.description20 pages, 2 EPS figures, published in Journal of Physics A
dc.identifierhttps://arxiv.org/abs/0801.4510
dc.identifierhttp://arxiv.org/abs/0801.4510
dc.identifierJ. Phys. A: Math. Theor. 41 235301 (2008)
dc.identifierdoi:10.1088/1751-8113/41/23/235301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163647
dc.subjectMathematical Physics
dc.subject81S05; 81S30; 33C45; 33C90; 37N20
dc.titleThe Wigner distribution function for the one-dimensional parabose oscillator
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