Darboux and Baecklund Transformations for the Schroedinger Equation

摘要

A Darboux transformation (DT) which can be used to get q sup 0 (x) bounded asymptotically from u sup 0 (x) bounded for any g(x) (where q(x) and u(x) are terms in a potential which is a solution to the Schroedinger equation) is introduced. It is shown how to recover the DT in a generalized form using a dressing method. The DT is used to obtain explicit solutions of the Schroedinger equation.