Second Order Darboux Displacements
Quantum Physics
2009-11-10 v1
Abstract
The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schroedinger equation equation are found for any value of the energy. A simple analytic expression for a family of two-gap potentials is derived.
Cite
@article{arxiv.quant-ph/0307146,
title = {Second Order Darboux Displacements},
author = {B F Samsonov and M L Glasser and J Negro and L M Nieto},
journal= {arXiv preprint arXiv:quant-ph/0307146},
year = {2009}
}