Inverse scattering with partial information on the potential

Loading...
Thumbnail Image

View/Download File

Persistent link to this item

Statistics
View Statistics

Journal Title

Journal ISSN

Volume Title

Title

Inverse scattering with partial information on the potential

Published Date

2001-02

Publisher

Type

Abstract

The one-dimensional Schröddinger equation is considered when the potential is real valued and integrable and has a finite first moment. The recovery of such a potential is analyzed in terms of the scattering data consisting of a reflection coefficient, all the bound-state energies, knowledge of the potential on a finite interval, and all of the bound-state norming constants except one. It is shown that a missing norming constant in the data can cause at most a double nonuniqueness in the recovery. In the particular case when the missing norming constant in the data corresponds to the lowest-energy bound state, the necessary and sufficient conditions are obtained for the nonuniqueness, and the two norming constants and the corresponding potentials are determined. Some explicit examples are provided to illustrate the nonuniqueness.

Keywords

Description

Replaces

License

Series/Report Number

Funding information

Isbn identifier

Doi identifier

Previously Published Citation

Suggested citation

Aktosun, Tuncay; Weder, Ricardo. (2001). Inverse scattering with partial information on the potential. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/3544.

Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.