Two new potentials for the free particle model

In this work, is proposed a very simple method for obtaining the generalize d potential associated with a known standard potential. The procedure is st raightforward because it only uses two Ricatti-type relationships as enough condition to find a generalized potential; one particular equation is need ed to identify the specific potential under study and one general Ricatti r elationship is used to find the corresponding generalized potential. Moreov er, the method is completely general due to the fact that an arbitrary pote ntial has been considered in its development for which the procedure can al so 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 t he free particle model. This work example leads to two new potentials whose Hamiltonians are isospectral when they are compared with the former Hamilt onian. (C) 1999 American Institute of Physics. [S0022-2488(99)03311-3].