Asymptotic behaviour of resonance eigenvalues of the Schrödinger operator with a matrix potential

Abstract

We will discuss the asymptotic behaviour of the eigenvalues of a Schrödinger operator with a matrix potential defined by the Neumann boundary condition in L₂^{m}(F), where F is a d-dimensional rectangle and the potential is an m×m matrix with m≥2, d≥2 , when the eigenvalues belong to the resonance domain, roughly speaking they lie near the planes of diffraction.

Keywords

• Schrödinger operator,Neumann condition,Resonance eigenvalue,Perturbation theory

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