PDE Seminar (2019/6/21): Eigenvalues and eigenfunctions of the two-dimensional Schrödinger operator with strong magnetic field

Date
2019-6-21 16:30 - 2019-6-21 17:30
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Naoya Yoshida (Ritsumeikan University)
 
We consider the spectrum of the two-dimensional Schrödinger operator with homogeneous magnetic field. The non-perturbed operator has eigenvalues with infinite multiplicity called Landau levels. The perturbation, which decays at infinity, may create eigenvalues with finite multiplicity around each Landau level. In this talk, we give the precise asymptotics of the eigenvalues near the minimum of the potential and the corresponding eigenfunctions as the strength of the magnetic field tends to infinity.