Applications of infinite order perturbation theory in linear systems. I

Abstract

The applicability of infinite order perturbation theory to linear systems is exhibited. The technique involves a generalization of the method developed by Wu and Taylor and can be used to study systems described by the equations of the following form V_nnu_n + V_n,n+1u_n+1 + V_n,n−1 × u_n−1 = Eu_n, where the coupling coefficients ${\mathrm{V\prime }}_{\mathrm{nn}}\text{'}\mathrm{s}$ depend on n. The wide range of application of the generalized method is demonstrated by using it to study systems as different as the plane rotator in an external field on the one hand and the dynamics of a disordered chain on the other.