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

Abstract

We will discuss the asymptotic behaviour of the eigenvalues of Schrödinger operator with a matrix potential defined by Neumann boundary condition in $L_2^m(F)$, where $F$ is $d$-dimensional rectangle and the potential is a $m\times m$ matrix with $m\ge 2$, $d\ge 2$ , when the eigenvalues belong to the resonance domain, roughly speaking they lie near planes of diffraction. \textbf{Keywords:} Schrödinger operator, Neumann condition, Resonance eigenvalue, Perturbation theory. \textbf{AMS Subject Classifications:} 47F05, 35P15

References in corpus (1)

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