Algebraic treatment of the confluent Natanzon potentials
Département de Physique, Faculté des Sciences,
Université Badji Mokhtar Annaba, Algérie
2 Département de Physique, Faculté des Sciences, Université Mentouri Route d'Ain El Bey, Constantine, Algérie
Accepted: 11 July 2000
Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas, the Green's function for the class of the confluent Natanzon potentials is constructed straightforwardly. The bound-state energy spectrum is then determined. Eventually, the three-dimensional harmonic potential, the three-dimensional Coulomb potential and the Morse potential may all be considered as particular cases.
PACS: 03.65.-w – Quantum mechanics / 03.65.Fd – Algebraic methods / 02.20.-a – Group theory
© EDP Sciences, 2000