The $q$-analogue of the Quantum Theory of Angular Momentum: a review from special functions
Renato \'Alvarez-Nodarse, Alberto Arenas-G\'omez
TL;DR
This paper reviews the $q$-analogue of quantum angular momentum theory, focusing on $su_q(2)$ and expressing Clebsch-Gordan coefficients via $q$-hypergeometric series, simplifying their properties.
Contribution
It provides a unified, simplified representation of Clebsch-Gordan coefficients in the $q$-deformed quantum angular momentum framework.
Findings
Representation of Clebsch-Gordan coefficients using $q$-hypergeometric series
Simplified derivation of properties of $q$-Clebsch-Gordan coefficients
Enhanced understanding of $su_q(2)$ algebra in quantum angular momentum
Abstract
In the present paper we review the -analogue of the Quantum Theory of Angular Momentum based on the -algebra , with a special emphasis on the representation of the Clebsch-Gordan coefficients in terms of -hypergeometric series. This representation allows us to obtain several known properties of the Clebsch-Gordan coefficients in an unified and simple way.
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Taxonomy
TopicsAdvanced Mathematical Identities · Algebraic structures and combinatorial models · Mathematical functions and polynomials