Abstract
The problem of finding eigenvalues of the static nonlinear Schr\"odinger equation with a potential is numerically investigated. The change of eigenfunctions resulting from the transformation of a potential well into a potential hill is studied. Unlike the linear Schr\"odinger equation, continuous and square-integrable solutions exist, not only for potential wells, but also for potential hills. For potential hills there may exist a few different eigenfunctions with the same number of nodes, whereas eigenfunctions for potential wells are single valued. Moreover, regions of stability are discovered where a continuum of eigenfunctions exist. In these regions, eigenfunctions may continuously transform one into another in certain energy intervals. The possible practical use of these solutions is discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physical review. A, Atomic, molecular, and optical physics
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.
