Clebsch-Gordan coefficients and Racah coefficients for the SU(2) and SU(1,1) groups as the discrete analogues of the Poschl-Teller potential wavefunctions

The Clebsch-Gordan coefficients (CGC) and the Racah coefficients for the SU(2) and SU(1,1) groups are studied as functions of a discrete variable. It has been shown that CGC for SU(2) and SU(1,1) groups may be considered to be discrete analogues of wavefunctions for the one-dimensional Schrodinger equation with the Poschl-Teller potential. Expressions for CGC and 6j-symbols of the SU(1,1) group have been found through the Hahn and Racah polynomials. Consideration is given to the asymptotic properties of eigenvalues and eigenfunctions of the Hamiltonian of an asymmetric top and of the Bargmann-Moshinsky operator Omega.