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Paper IPM / P / 6924  


Abstract:  
A wide range of 1D shape invariant potentials lie in two different classes. In either of these classes the quantum states are distinguished by both of the main and the secondary quantum numbers n and m. We show that quantum states of the first and of the second classes represent shape invariance with respect to n and m, respectively. We also analyze the relationship between these two classes with Lie algebra sl(2,c).
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