Darboux transformations and supersymmetrization procedures (Q678634)

This note is concerned with the construction of solutions of the Sturm-Liouville equation \[ -\psi_{xx}+ u(x)\psi= \lambda\psi. \] The authors discuss the Darboux's transformation -- or, in an equivalent way, the factorization method -- in connection with two procedures of super-symmetrization available in two- and three-dimensional spaces, namely the standard and the spin-orbit coupling procedures.