Clebsch-Gordan Coefficients: A Quantum Mechanical and Mathematical Perspective

In this work, Clebsch-Gordan coefficients are studied from both a quantum mechanical and a mathematical perspective. In quantum mechanics, Clebsch-Gordan coefficients arise when two quantum systems with a certain angular momentum are combined and the total angular momentum is to be found. We start by discussing the relevant postulates of quantum...

Quantum Analogs of Tensor Product Representations of su(1; 1)*

Abstract. We study representations of Uq(su(1; 1)) that can be considered as quantum analogs of tensor products of irreducible -representations of the Lie algebra su(1; 1). We determine the decomposition of these representations into irreducible -representations of Uq(su(1; 1)) by diagonalizing the action of the Casimir operator on suitable...