Asymptotic bounds on the number of the eigenvalues in the gaps of the 2D magnetic Schrödinger operator

Article type: Research Article

Authors:

Affiliations: Section of Mathematical Physics, Institute of Mathematics, Bulgarian Academy of Sciences, P.O. Box 373, 1090 Sofia, Bulgaria

Abstract: We consider the two‐dimensional Schrödinger operator with generically bounded magnetic field, perturbed by a scalar potential -gV, g \geq 0 being the coupling constant. We assume that V is non‐negative and decays rapidly at infinity (e.g., V({\mathbf x})\asymp \vert{\mathbf x}\vert^{-\alpha}, \alpha > 2, as \vert{\mathbf x}\vert\rightarrow \infty). We examine the asymptotic behaviour as g \rightarrow \infty of the eigenvalues situated in the gaps of the spectrum of the unperturbed operator.

Journal: Asymptotic Analysis, vol. 16, no. 2, pp. 87-98, 1998