GROUND-STATE ENERGY OF AN EXCITON-(LO) PHONON SYSTEM IN 2 AND 3 DIMENSIONS - GENERAL OUTLINE AND 3-DIMENSIONAL CASE

This paper presents a variational study of the ground-state energy of an exciton-phonon system in two or three spatial dimensions. The excit on-phonon interaction is of Frohlich type. Making use of functional-in tegral techniques, the phonon part of the problem can be eliminated ex actly, leading to an effective two-particle problem, which has the sam e spectral properties as the original one. Subsequently, we apply Jens en's inequality to obtain upper bounds on the ground-state energy. The paper has two major intentions: First, we demonstrate for the problem under consideration that one can profitably use a nonharmonic trial a ction within the functional-integral framework. The corresponding vari ational bounds an the ground-stare energy compare favorably with all p revious ones. Second, we show that the lowest bound is an analytical f unction of the electron-phonon coupling parameter and completely smoot h throughout the whole parameter region. This is in contrast to previo us variational findings, but consistent with rigorous qualitative resu lts for the true groundstate energy.