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.
Bibliographical noteFunding Information:
Supported by KAMEA Project for scientific Absorption in Israel and partially by the German-Israeli Foundation (GIF), grant number I-619-17.6/2001.
- Discrete part of the spectrum
- Essential spectrum
- Perturbation of a periodic potential
- Schrödinger operator
ASJC Scopus subject areas
- Algebra and Number Theory