par Del Sol Mesa, Antonio;Quesne, Christiane 
;Smirnov, Yu
Référence Journal of Physics A: Mathematical and General, 31, 1, page (321-335)
Publication Publié, 1998-01
;Smirnov, YuRéférence Journal of Physics A: Mathematical and General, 31, 1, page (321-335)
Publication Publié, 1998-01
Article révisé par les pairs
| Résumé : | We study in detail the bound-state spectrum of the generalized Morse potential (GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the corresponding Schrödinger equation with the Laplace equation on the hyperboloid and the Schrödinger equation for the Pöschl-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(1, 1) ⊕ su(1, 1). We prove that some of the so(2, 2) generators connect among themselves wavefunctions belonging to different GMPs (called satellite potentials). The conserved quantity is some combination of the potential parameters 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 calculation of Frank-Condon factors for electromagnetic transitions between rovibrational levels based on different electronic states. |
