The problem of interacting Einstein phonons is treated by deriving the Green function through a functional derivative approach employing the Hamiltonian of Born-von Kaacute;rmán. In this case the Dyson equation yields an exact solution for the Green function whose poles are the frequency versus wave vector dispersion relation. The Green function is used to calculate the internal energy and the Helmholtz free energy of the crystal. The latter is derived by integrating the average interaction energy over the coupling parameter.

This content is only available via PDF.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.