Representation of the quantum algebra $S{U}_q(2)$ in the basis with diagonal $"J_x"$ generator

Abstract

Generators of the quantum $S{U}_q(2)$ algebra are obtained in the explicit form in the basis where the operator $\exp \frac{J_z}{2}{J}_x\exp \frac{J_z}{2}$ is diagonal. It is shown that the solution of this problem is related to the representation theory of the two-dimensional algebra $[s,r]=\tanh t(s^2-r^2+1)$. The relevance of such basis to some problems of quantum optics is discussed.

LaTeX, 10 pages