Darboux-Witten techniques for the Demkov-Ostrovsky problem

Abstract

The bosonic strictly isospectral problem for Demkov-Ostrovsky (DO) effective potentials in the radially nodeless sector is first solved in the supersymmetric Darboux-Witten (DW) half line (or l-changing) procedure. As an application, for the κ=1 class, if one goes back to optics examples, it might be possible to think of a one-parameter family of Maxwell lenses having the same optical scattering properties in the nodeless radial sector. Although the relative changes in the index of refraction that one may introduce in this way are at the level of several percents, at most, for all DO orbital quantum numbers l\geq 0, the index profiles are different from the original Maxwell one, possessing an inflection point within the lens. I pass then to the DW full line (or N-changing) procedure, obtaining the corresponding Morse-type problem for which the supersymmetric results are well established, and finally come back to the half line with well-defined results