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Paper   IPM / Physic / 7625
School of Physics
  Title:   Extended Supersymmetry for the Bound States of the Generalized Hulthen Potential Hierarchy
1.  H. Fakhri
2.  A. Chenaghlou
  Status:   Published
  Journal: J. Phys. A: Math. Gen.
  Vol.:  37
  Year:  2004
  Pages:   8545-8559
  Supported by:  IPM
Using the associated hypergeometric differential equation, we solve analytically the bound states corresponding to a hierarchy of the radial potential −v0 e−δr/(1−e−δr) + c e−δr / (1−e−δr)2 as a generalisation of the Hulthén potential. Then, an analytic solution corresponding to a special case for which the parameter c is expected to be in terms of l(l+1) is also derived. Meanwhile without introducing a superpotential and in the framework of supersymmetric quantum mechanics, it is shown that these bound states can be calculated by two different algebraic methods. Based on these two approaches, it is noticed that the bound states realise an extended supersymmetry structure.

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