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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Tensor operator formulation of Weyl-ordered polynomials

Max A. Lohe, Lawrence C. Biedenharn, James D. Louck

Published Jan 15, 1991• 13 citations
Publisher

Abstract

Weyl-ordered polynomials, which have been used recently to solve quantum-mechanical models, are shown to be equivalent to symplecton polynomials defined previously as components of a tensor operator in SU(2). These polynomials are shown to be expressible in terms of hypergeometric functions of argument -1, providing thereby a direct derivation of their properties.

DOI
10.1103/physrevd.43.617

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Weyl-ordered polynomials, which have been used recently to solve quantum-mechanical models, are shown to be equivalent to symplecton polynomials defined previously as components of a tensor operator in SU(2). These polynomials are shown to be expressible in terms of hypergeometric functions of argument -1, providing thereby a direct derivation of their properties.
We investigate the properties of the Weyl-ordered polynomials Tm,n by the technique of integration within a Weyl-ordered product (IWWOP) and the Weyl quantization rule. The introduction of the Weyl-ordering symbol ⋮⋮ and the IWWOP provide us with a convenient approach for deriving the Weyl-ordered form of the product of Tm,n and other operators. The Weyl-ordered Dirac's δ-function form of the Wigner operator can also directly lead us to the Weyl quantization formalism for the functions of radial vaiables.