Self-Energy of the Polaron for Intermediate Temperatures

Abstract

Approximate eigenvalues of the Fröhlich Hamiltonian, used as a model to represent the behavior of the electron coupled to the optical modes of an ionic crystal, are obtained for temperatures at which there is an appreciable probability of real phonons being present in the field. The method used is an extension of the variational technique employed by Gurari to obtain the eigenvalues at absolute zero. Correlations between phonons are neglected. The results obtained indicate that an electron in equilibrium with the lattice will have a strongly temperature-dependent effective mass for intermediate temperatures.