Location of eigenvalues of Schrödinger operators with matrix-valued potentials

he matrix potential appears in the Pauli operator, when the spin-magnetic interaction is involved. The non-self-adjoint potentials knowledge is required for the formulation of non-Hermitian quantum mechanics. Therefore our goal is to generalize a known estimation for complex and matrixvalued potentials. We recall the derivation of the estimation for Schrodinger's operators with scalar potentials, namely the use of the symmetrical Birman-Schwinger technique, the derivation of Green's function and the proof of the optimality of the estimation. Subsequently, we apply this procedure to the matrix potentials and derive a general estimate of non-positive eigenvalues.