Abstract
This paper is devoted to the semiclassical magnetic Laplacian. Until now WKB expansions for the eigenfunctions were only established in the presence of a non-zero electric potential. Here we tackle the pure magnetic case. Thanks to Feynman–Hellmann type formulas and coherent states decomposition, we develop here a magnetic Born–Oppenheimer theory. Exploiting the multiple scales of the problem, we are led to solve an effective eikonal equation in pure magnetic cases and to obtain WKB expansions.We also investigate explicit examples for which we can improve our general theorem: global WKB expansions, quasi-optimal Agmon estimates and upper bound of the tunelling effect (in symmetric cases).We also apply our strategy to get more accurate descriptions of the eigenvalues and eigenfunctions in a wide range of situations analyzed in the last two decades.
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 callDisclaimer: 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.
