General form of the Green’s function regular at infinity for the homogeneous Sturm–Liouville matrix operator

摘要

The standard Fourier transform method is used to analyze the expression of the Green’s function regular at infinity for the Sturm–Liouville matrix operator in the important case of position independent parameters. A quadratic eigenvalue and eigenvector problem appears naturally. The classification of the former problem solutions allows to obtain the Green’s function in a compact general form. Different physical problems were analyzed and the corresponding Green’s function for various elementary excitations in less studied systems was predicted also.