AbstractIn phonon Green's function theory two representations of the defect matrix operator are used, a frequency‐dependent and a frequency‐independent. Care has to be taken when changing from one definition to the other: Not all results are independent of the definition chosen. Since such dependencies are not mentioned in the literature, one may be easily misled, e.g. in numerical calculations. Therefore a systematic comparison of the two representations is given. The theory is applied to the calculation of the defect density of states for mass defects in the polyethylene chain.