Abstract
AbstractPerturbation theory conventionally is applied either to one‐particle Green functions (or to equivalent quantities) directly or to their inverses, i.e. to the self‐energies. Both methods, however lead to wrong, in the first case even to negative and divergent, densities of states in the corresponding order. Here the system of equations for the Green functions is solved exactly in the standard form G = N/D and perturbation theory is applied to both, the nominator N and the denominator D separately. It is shown that this method is free of divergencies and results in the correct density of states in each order. This new perturbation theory is especially suited for the calculation of electron and phonon spectra of superlattices.
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