Eigenvalue Asymptotics for the Schrödinger Operator with a Matrix Potential in a Single Resonance Domain

Abstract

We consider a Schrödinger Operator with a matrix potential defined in $L_2^m(F)$ by the differential expression\begin{equation*} L(ϕ(x))=(-Δ+V(x))ϕ(x) \end{equation*}and the Neumann boundary condition, where $F$ is the $d$ dimensional rectangle and $V$ is a martix potential, $m⩾2,d⩾2$. We obtain the asymptotic formulas of arbitrary order for the single resonance eigenvalues of the Schrödinger operator in $L_2^m(F)$.

Presented by Setenay Akduman in the International Conference "Analysis, Topoogy and Applications (ATA 2014)", Vrnjačka Banja, Serbia, May 26-29, 2014, Keywords: Schrödinger operator, Neumann condition, perturbation, matrix potential

Cited by in corpus (1)

• Asymptotic Behaviour of Resonance Eigenvalues of the Schrödinger operator with a Matrix Potential