Abstract
We consider the Generalized Heisenberg Algebra (GHA) and the deformed GHA with finite representations. We provide the necessary restriction on the characteristic function of the periodic GHA and that of the periodic deformed GHA and study particular examples. Then, we give a deformation of GHA raising operator of the Morse system and conclude that this system can be described by a periodic deformed GHA as it can be deduced from a nilpotent GHA.
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