Raising and Lowering of Generalized Hulthén Potential from Supersymmetry Approaches

We obtain the exact bound states of the generalized of Hulthén potential with negative energy levels using an analytic approach. In order to obtain bound states, we use the associated Jacobi differential equation. Using the supersymmetry approach to quantum mechanics, we show that these bound states, via four pairs of first order differential operators, represent four types of ladder equations. Two types of these supersymmetric structures suggest derivation of algebric solutions for the bound states using two different approaches. PACS 21.60.Cs; 21.60.Fw; 21.60.-n; 03.65.Fd; 03.65.Ge; 03.65.-w