In this work, is proposed a very simple method for obtaining the generalized potential associated with a known standard potential. The procedure is straightforward because it only uses two Ricatti-type relationships as enough condition to find a generalized potential; one particular equation is needed to identify the specific potential under study and one general Ricatti relationship is used to find the corresponding generalized potential. Moreover, the method is completely general due to the fact that an arbitrary potential has been considered in its development for which the procedure can also be used to find new potentials which could be needed in the modeling of important quantum interactions. The usefulness of the proposed approach, is shown with the treatment of the three- and one-dimensional potential for the free particle model. This work example leads to two new potentials whose Hamiltonians are isospectral when they are compared with the former Hamiltonian.

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