Abstract
We study the spectral properties of the Schrödinger operator with a constant electric field perturbed by a bounded potential. It is shown that if the derivative of the potential in the direction of the electric field is smaller at infinity than the electric field, then the spectrum of the corresponding Stark operator is purely absolutely continuous. In one dimension, the absolute continuity of the spectrum is implied by just the boundedness of the derivative of the potential. The sharpness of our criterion for higher dimensions is illustrated by constructing smooth potentials with bounded partial derivatives for which the corresponding Stark operators have a dense point spectrum.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.