| Abstract: | The exponential transformation, developed in an earlier paper 1], is applied to the Hamiltonian of a linear harmonic chain with a molecular defect. The resulting eigenvalue equation is solved for the localized frequency. A discussion of the renormalized in-band frequencies shows that in good approximation the entire Hamiltonian is diagonalized by a single transformation. This is of great advantage, since in the classical Lifshitz formalism each single frequency has to be evaluated separately. Furthermore, a simpler transformation is discussed, which is derived from an U-matrix formalism. Numerical results of the two transformations are given for a chain with 999 lattice points and compared with the exact values from the classical Lifshitz formalism. |
