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Paper   IPM / Physic / 7766
School of Physics
  Title:   Shape Invariant Natanzon Potential Hierarchy and Its Twin: A Novel Approach
1.  H. Fakhri
2.  A. R. Chenaghlou
  Status:   Published
  Journal: Phys. Lett. A
  Vol.:  337
  Year:  2005
  Pages:   374-383
  Supported by:  IPM
Shape invariant supersymmetric partner potentials corresponding to the Natanzon superpotential Atanh γrB coth γr and its twin i.e. −(A + B)tanh γrB sech γr csch γr are obtained as 2-fold hierarchies whose solutions are a common set of the quantum states. It is shown that they are derived by using simultaneous laddering relations with respect to two different parameters n and m of some associated Gegenbauer functions via two different methods including (a) simultaneous increasing or decreasing of the parameters, and (b) increasing one of the parameters and decreasing the other one. The shape invariance condition in the concept of Gendenshtein on the 2-fold hierarchies of supersymmetric partner potentials with respect to the parameters n and m is inherited from those laddering relations by two different ways.

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