dorsal/arxiv
View SchemaGroup Theory and Quasiprobability Integrals of Wigner Functions
| Authors | A. J. Bracken, D. Ellinas, J. G. Wood |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304010 |
| URL | https://arxiv.org/abs/quant-ph/0304010 |
| DOI | 10.1088/0305-4470/36/20/102 |
Abstract
The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0,1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric disks and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in Hilbert space carrying the positive discrete series representations of the algebra su(1,1)or so(2,1). The explicit relation between the spectra of operators associated with disks and circles with proportional radii, is given in terms of the dicrete variable Meixner polynomials.
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"abstract": "The integral of the Wigner function of a quantum mechanical system over a\nregion or its boundary in the classical phase plane, is called a\nquasiprobability integral. Unlike a true probability integral, its value may\nlie outside the interval [0,1]. It is characterized by a corresponding\nselfadjoint operator, to be called a region or contour operator as appropriate,\nwhich is determined by the characteristic function of that region or contour.\nThe spectral problem is studied for commuting families of region and contour\noperators associated with concentric disks and circles of given radius a. Their\nrespective eigenvalues are determined as functions of a, in terms of the\nGauss-Laguerre polynomials. These polynomials provide a basis of vectors in\nHilbert space carrying the positive discrete series representations of the\nalgebra su(1,1)or so(2,1). The explicit relation between the spectra of\noperators associated with disks and circles with proportional radii, is given\nin terms of the dicrete variable Meixner polynomials.",
"arxiv_id": "quant-ph/0304010",
"authors": [
"A. J. Bracken",
"D. Ellinas",
"J. G. Wood"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/36/20/102",
"title": "Group Theory and Quasiprobability Integrals of Wigner Functions",
"url": "https://arxiv.org/abs/quant-ph/0304010"
},
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