Abstract.
We study the spectrum of the one-dimensional Schrödinger operator with a potential, whose periodicity is violated via a local dilation. We obtain conditions under which this violation preserves the essential spectrum of the Schrödinger operator and an infinite number of isolated eigenvalues appear in a gap of the essential spectrum. We show that the considered perturbation of the periodic potential is not relative compact in general.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zelenko, L. Spectrum of the One-dimensional Schrödinger Operator With a Periodic Potential Subjected to a Local Dilative Perturbation. Integr. equ. oper. theory 58, 573–589 (2007). https://doi.org/10.1007/s00020-007-1515-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00020-007-1515-z