Generalized radial potentials: hydrogenic and isotonic interaction models

In this work, we present a very useful procedure to generalize any specific radial potential or to generate new models of interaction potentials. The proposed approach basically takes into consideration the use of three well- established relationships: the first one is used to identify the particular radial potential under study; the second to find a modified radial potenti al; and the third to obtain the corresponding generalized radial potential. As expected, it is shown that the modified and generalized radial potentia ls are isospectral with respect to the particular or former potential Hamil tonian. As a useful application of the proposed method, we give the explici t treatment of the generalized hydrogenic and isotonic potentials. Moreover , the proposed procedure is general because it considers any arbitrary radi al potential, which indicates that the approach can be easily applied to ob tain the generalization of any other known radial potential, as well as to find new potentials that can be advantageously used for modeling important quantum interactions. Further, the displayed procedure includes the particu lar case l = 0 for one-dimensional isospectral potentials for which the pro posed approach can be considered as an improvement of any particular method developed with the Same purpose. (C) 1999 Elsevier Science B.V. All rights reserved.