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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics