Physics – Mathematical Physics
Scientific paper
2004-03-25
J.Phys.A37:4267-4281,2004
Physics
Mathematical Physics
22 pages, no figure. Archive version is already official. Published by JPA at http://stacks.iop.org/0305-4470/37/4267
Scientific paper
10.1088/0305-4470/37/14/006
We show that there exist some intimate connections between three unconventional Schr\"odinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space, respectively. This occurs whenever a specific relation between the deforming function, the position-dependent mass and the (diagonal) metric tensor holds true. We illustrate these three equivalent approaches by considering a new Coulomb problem and solving it by means of supersymmetric quantum mechanical and shape invariance techniques. We show that in contrast with the conventional Coulomb problem, the new one gives rise to only a finite number of bound states.
Quesne Christiane
Tkachuk Volodymyr M.
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