The shifted harmonic approximation and asymptotic SU(2) and SU(1,1) Clebsch--Gordan coefficients

Abstract

Clebsch-Gordan coefficients of SU(2) and SU(1,1) are defined as eigenfunctions of a linear operator acting on the tensor product of the Hilbert spaces for two irreps of these groups. The shifted harmonic approximation is then used to solve these equations in asymptotic limits in which these eigenfunctions approach harmonic oscillator wave functions and thereby derive asymptotic expressions for these Clebsch--Gordan coefficients.