GROUND-STATE ENERGY OF FRÖHLICH ELECTRON-PHONON SYSTEM

Abstract
Recently Feynman's path-integral formalism of the Fröhlich optical polaron problem is generalized, by which it is easy and natural to get the second-order perturbation result in the weak-coupling case and the Pekar's result in the strongcoupling case, even in the crudest ground-state approximation. By using numerical method to the equations which are given by the ground-state approximation, the ground-state energy of the electron-optical phonon system can obtained for the overall range of coupling strength. In addition, a self-consistent set of equations is derived for a central optimized potential without using the ground-state approximation. This effective local, central potential is the solution of a linear integral equation which was similar to the extensive work of optimized-potential model (OPM) in atomic physics. By using OPM formalism, no particular choice of interaction form is taken, therefore, except the approximation by Jensen's inequality, the ground-state energy of the electron-optical phonon interacting system can be obtained without any approximation.