Supersymmetry and Darboux Transformations for the Generalized Schr_dinger Equation

摘要

We construct Darboux transformations for a generalized Schr_dinger equation by means of the intertwining operator method. We establish a relation between first-order Darboux transformations, supersymmetry, and factorization of the I Iamiltonians that are associated with our generalized Schr_dinger equation. Furthermore, our methods allow for the generation of isospectral potentials, where one of the potentials has additional or less hound states than its partner. In the particular case of a conventional Schr_dinger equation our generalized Darboux transformations reduce correctly to the well-known ex_pressions.