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

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We consider a Schrödinger Operator with a matrix potential defined in L₂ᵐ(F) by the differential expressionequation* L(ϕ(x))=(-Δ+V(x))ϕ(x) 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 L₂ᵐ(F).