The Wigner distribution function for the one-dimensional parabose oscillator

Abstract

In 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.

20 pages, 2 EPS figures, published in Journal of Physics A

References in corpus (7)

• Quantum gravity and minimum length
• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Quantum state reconstruction of the single-photon Fock state
• Quantum mechanics on the noncommutative plane and sphere
• Quantum Groups and Their Applications in Nuclear Physics
• Observations on noncommuting coordinates and on fields depending on them
• The Wigner function of a q-deformed harmonic oscillator model

Cited by in corpus (11)

• Finite oscillator models: the Hahn oscillator
• The su(2)_α Hahn oscillator and a discrete Hahn-Fourier transform
• The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials
• The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass
• A finite oscillator model related to sl(2|1)
• Discrete series representations for sl(2|1), Meixner polynomials and oscillator models
• The Husimi function of a semiconfined harmonic oscillator model with a position-dependent effective mass
• Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra $\mathfrak{osp}\left(1|2\right)$: exact solution for the quantum harmonic oscillator with a position-dependent mass
• Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass
• Impact of the non-canonical approach to the exact solution of the ideal one-dimensional electron gas confined with an anisotropic quantum wire of oscillator-shaped profile
• The intensity of the random variable intercept in the sector of negative probabilities