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| Paper IPM / P / 7337 | ||||||||||||||||||
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Using shape invariance symmetries with respect to two different parameters n and m, we derive the general forms of the partner Hamiltonians for the superpotentials Atanhωy + B/A and −Acotωθ+ B cscωθ, respectively. For the first model in a special case and the second model in the general case, the parameters m and n play the role of the quantization numbers for the spectrum and quantum states as finite and infinite ones, respectively. We also get a type of the shape invariance symmetry which is realized by the operators shifting only m and only n, respectively for two models. Furthermore, for the models, other shape invariance symmetries based on the operators shifting the indices n and m of quantum states simultaneously and inversely as well as simultaneously and agreeably are derived.
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