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

We will discuss the asymptotic behaviour of the eigenvalues of Schr\"{o}dinger 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 \(m\geq 2\), \(d\geq 2\) , when the eigenvalues belong to the resonance domain, roughly speaking they lie near planes of diffraction. \textbf{Keywords:} Schr\"{o}dinger operator, Neumann condition, Resonance eigenvalue, Perturbation theory. \textbf{AMS Subject Classifications:} 47F05, 35P15