Eigenvalues and eigenfunctions for the two dimensional Schrödinger operator with strong magnetic field

Article type: Research Article

Authors: Yoshida, Naoya^{; *}

Affiliations: Graduate School of Science and Engineering, Ritsumeikan University, 1-1-1 Noji-Higashi Kusatsu 525-8577, Japan. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We study the eigenvalues of the two-dimensional Schrödinger operator with a large constant magnetic field perturbed by a decaying scalar potential. For each Landau level, we give the precise asymptotic distribution of eigenvalues created by the minimum, maximum and the closed energy curve of the potential. Normal form reduction, WKB construction and pseudodifferential calculus are applied to the effective Hamiltonian.

Keywords: Landau level, effective Hamiltonian, WKB construction, pseudodifferential calculus, Bohr–Sommerfeld quantization condition

DOI: 10.3233/ASY-191585

Journal: Asymptotic Analysis, vol. 120, no. 1-2, pp. 175-197, 2020