GENERALIZED MORSE POTENTIAL - SYMMETRY AND SATELLITE POTENTIALS

We study in detail the bound-state spectrum of the generalized Morse p otential (GMP), which was proposed by Deng and Fan as a potential func tion for diatomic molecules. By connecting the corresponding Schroding er equation with the Laplace equation on the hyperboloid and the Schro dinger equation for the Poschl-Teller potential, we explain the exact solvability of the problem by an so(2, 2) symmetry algebra, and obtain an explicit realization of the latter as su(l, 1) circle plus su(l, 1 ). We prove that some of the so(2, 2) generators connect among themsel ves wavefunctions belonging to different GMPs (called satellite potent ials). The conserved quantity is some combination of the potential par ameters instead of the level energy, as for potential algebras. Hence, so(2, 2) belongs to a new class of symmetry algebras. We also stress the usefulness of our algebraic results for simplifying the calculatio n of Frank-Condon factors for electromagnetic transitions between rovi brational levels based on different electronic states.