The generalized Hulthen potential

A generalization of the Hulthen potential is presented on the basis of an a pproach that uses the factorization of a general Hamiltonian by means of a specific model of operational equations with the structure similar to beta( p)(r) -/+ (d/dr). To achieve this goal, the treatment of the V-Hs(r) standa rd Hulthen potential for bound s states is carried out by proposing a parti cular beta(p)(r) ansatz to identify V-Hs(r) by means of a particular Riccat i-type relationship. Once the identification has been achieved, the general ized Hulthen potential is obtained straightforwardly with the aid of a gene ral Riccati formula. As expected, the Hamiltonian of the generalized Hulthe n potential is isospectral when compared with the corresponding standard Ha miltonian. Moreover, according to the Darboux transform there exists a modi fied Hulthen potential which is also isospectral. We show that the latter i s just a particular case of the generalized Hulthen interaction model.