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Bulgarian Journal of Physics
Print: 1310-0157 Online: 1314-2666
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RECOGNIZED BY THE EUROPEAN PHYSICAL SOCIETY 
Bulg. J. Phys. vol.20 no.3-4 (1993), pp. 001-010
Algebraic Solution for Specific Potentials on the Poincare Upper Half-Plane
L. Chetouani1, L. Guechi1, T.F. Hammann2
1Départment de Physique Théorique, Institut de Physique, Université de Constantine, Constantine, Algeria
2Laboratoire de Mathématiques, Physique Matématique et Informatique, Faculté des Sciences et Techniques, Université de Haute Alsace, 4, rue des Frères Lumière, F68093 Mulhouse, France
go back1Départment de Physique Théorique, Institut de Physique, Université de Constantine, Constantine, Algeria
2Laboratoire de Mathématiques, Physique Matématique et Informatique, Faculté des Sciences et Techniques, Université de Haute Alsace, 4, rue des Frères Lumière, F68093 Mulhouse, France
Abstract. The SO(2,1) Lie algebra is applied to certain specific potentials on the Poincare upper half-plane and the related Green's functions are hence constructed. The oscillator-like potential Green's function may be obtained straight away, whereas the Green's functions related to the Coulomb-like potential or to a constant external magnetic field vector? potential, can be accurately calculated by association with the Morse potential, through straight forward transformations. The energy spectrum for each potential is then deduced.