The Clebsch-Gordan coefficients for the covering of the (2 + 1)-Lorentz group in the parabolic basis

Debabrata Basu and Kurt Bernardo Wolf

Physica A: Statistical Mechanics and its Applications, 1982, vol. 114, issue 1, 472-476

Abstract: We report on work in which we build the generalized oscillator algebra, an SO (2, 1) algebra of second-order differential operators with a specified domain, realizing all self-adjoint irreducible representations belonging to the discrete or the continuous series. The diagonal subalgebra of the direct sum of two such algebras leads to the definition of product and coupled states, whose inner product provides the Clebsch-Gordan coefficients. These are obtained as solutions to (multichart) Schrödinger equations for Pöschl-Teller potentials, which involve at most Gauss hypergeometric function 2F1.

Date: 1982
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:114:y:1982:i:1:p:472-476

DOI: 10.1016/0378-4371(82)90335-1

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