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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 $A\tanh \omega y + B/A$ and $-A\cot \omega \theta + B \csc \omega \theta$, 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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