arXiv subjects

Renato Álvarez-Nodarse

Publications and source records attributed to Renato Álvarez-Nodarse.

2 recordsLinked to original sources

arXiv2022

The $q$-analogue of the Quantum Theory of Angular Momentum: a review from special functions

In the present paper we review the $q$-analogue of the Quantum Theory of Angular Momentum based on the $q$-algebra $su_q(2)$, with a special emphasis on the representation of the Clebsch-Gordan coefficients in terms of $q$-hypergeometric series. This representation allows us to obtain several known properties of the Clebsch-Gordan coefficients in an unified and simple way.

math.QA↗

arXiv2013

Using D-operators to construct orthogonal polynomials satisfying higher order q-difference equations

Let $(p_n)_n$ be either the $q$-Meixner or the $q$-Laguerre polynomials. We form a new sequence of polynomials $(q_n)_n$ by considering a linear combination of two consecutive $p_n$: $q_n=p_n+β_np_{n-1}$, $β_n\in \RR$. Using the concept of $\D$-operator, we generate sequences $(β_n)_n$ for which the polynomials $(q_n)_n$ are orthogonal with respect to a measure and common eigenfunctions of a higher order $q$-difference operator.

math.CA↗