A new formalism is presented, which has not the difficulties of the conventional Green's function methods for disturbed lattice dynamics. The new method introduces a Green's function and an eigenvector-function, which are defined in the whole ω-plane. A simple device allows to extract the conventional eigenvectors and eigenfrequencies from the eigenvector-function. A Green's function formalism and a random-phase assumption make it possible to calculate the disturbed eigenvector-function from the undisturbed one in such a way that both are normalized to the respective density of frequencies. The formalism thus is well-fit to describe changes of the density of frequencies, shifts of the bands and discrete (localized) solutions outside the bands. Applicability to the elastic continuum and quantum mechanics seem also possible.