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Paper   IPM / P / 7337
School of Physics
  Title:   Shape Invariance Symmetries for Quantum States of the Superpotentials Atanhωy + B/A and −Acotωθ+ B cscωθ
  Author(s):  H. Fakhri
  Status:   Published
  Journal: Phys. Lett. A
  Vol.:  324
  Year:  2004
  Pages:   366-377
  Supported by:  IPM
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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