Nonlocal supersymmetric deformations of periodic potentials
Quantum Physics
2008-11-26 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
Irreducible second-order Darboux transformations are applied to the periodic Schrodinger's operators. It is shown that for the pairs of factorization energies inside of the same forbidden band they can create new non-singular potentials with periodicity defects and bound states embedded into the spectral gaps. The method is applied to the Lame and periodic piece-wise transparent potentials. An interesting phenomenon of translational Darboux invariance reveals nonlocal aspects of the supersymmetric deformations.
Cite
@article{arxiv.quant-ph/0303051,
title = {Nonlocal supersymmetric deformations of periodic potentials},
author = {David J. Fernandez C. and Bogdan Mielnik and Oscar Rosas-Ortiz and Boris F. Samsonov},
journal= {arXiv preprint arXiv:quant-ph/0303051},
year = {2008}
}
Comments
15 pages, latex, 9 postscript figures