Extended supersymmetry for the bound states of the generalized Hulthén potential hierarchy

Using the associated hypergeometric differential equation, we analytically solve the bound states corresponding to a hierarchy of the radial potential ?v0 e??r/(1 ? e??r) + c e??r/(1 ? e??r)2 as a generalization of the Hulth?n 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 noted that the bound states realize an extended supersymmetry structure.