FINITENESS OF THE NEGATIVE SPECTRUM OF THE ONE-DIMENSIONAL MAGNETIC SCHRÖDINGER OPERATOR

In the paper we find relation between the solutions of the basic homogeneous equation of perturbation theory and eigen functions of a self-adjoint magnetic Schrödinger operator responding to negative eigenvalues. Under certain conditions on magnetic and electric potentials, we prove finiteness of the negative spectrum of the one-dimensional magnetic Schrödinger operator.