The Wigner distribution function for the one-dimensional parabose oscillator

Jafarov, E. and Lievens, S.J. and van der Jeugt, Joris (2008) The Wigner distribution function for the one-dimensional parabose oscillator. Journal of Physics A: Mathematical and Theoretical, 41 (23 (Article no. 235301)). ISSN 1751-8113. (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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In the beginning of the 1950s, 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 paper, we consider which definition for such a 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.

Item Type: Article
Subjects: Q Science
Divisions: Faculties > Science Technology and Medical Studies > School of Computing
Depositing User: Jane Griffiths
Date Deposited: 22 Apr 2009 13:26
Last Modified: 23 May 2014 13:00
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