On the eigenvalues for slowly varying perturbations of a periodic Schr\"{o}dinger operator
Marx, Magali
arXiv, 0503031 / Harvested from arXiv
Text on arXiv
In this paper, I consider one-dimensional periodic Schr{\"o}dinger operators perturbed by a slowly decaying potential. In the adiabatic limit, I give an asymptotic expansion of the eigenvalues in the gaps of the periodic operator. When one slides the perturbation along the periodic potential, these eigenvalues oscillate. I compute the exponentially small amplitude of the oscillations.
Publié le : 2005-03-12
Classification:  Mathematical Physics,  34E05, 34E20, 34L05, 34L40 
@article{0503031,
     author = {Marx, Magali},
     title = {On the eigenvalues for slowly varying perturbations of a periodic
  Schr\"{o}dinger operator},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0503031}
}

Marx, Magali. On the eigenvalues for slowly varying perturbations of a periodic
  Schr\"{o}dinger operator. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0503031/