Eigenvalue Asymptotics for the Schr\"odinger Operator with a Matrix Potential in a Single Resonance Domain

Sedef Karakłlłç; Setenay Akduman

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arXiv · 1409.4718

Eigenvalue Asymptotics for the Schr\"odinger Operator with a Matrix Potential in a Single Resonance Domain

Sedef Karakłlłç·Setenay Akduman

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Abstract

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

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BibTeX RIS

Sedef Karakłlłç, Setenay Akduman. 2014-09-16. Eigenvalue Asymptotics for the Schr\"odinger Operator with a Matrix Potential in a Single Resonance Domain. https://arxiv.org/abs/1409.4718

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